Malachi 4:2 (NKJ)
The "winged sun-disk" is a symbol originating in Assyria and Egypt and has been used by a variety of groups such as Freemasonry, Spiritists, Theosophy, the Rosicrucians and the Bible Students (JWs). This symbol has been called by numerous names such as the winged globe, winged-solar-disk, sun's disc, etc. This symbol was placed on numerous Bible Student material including editions of Russell's Studies in the Scriptures from about 1911 to 1920. Under Rutherford's leadership this symbol was eliminated from JW literature as it was viewed as being like the Pyramid &endash; it was Satanic, they said.
Origins and Use of the Winged Sun-Disk
This symbol apparently originated with the Assyrians but is most identified with the Egyptians. It is a ubiquitous symbol found in numerous forms on temples, etc. in Egypt. What exactly is it? What does it symbolize? What was it used for?
In the book Practical Egyptian Magic by Murray Hope it is said about this symbol and its use in Egypt:
Emblematic of the element of air, this consists of a circle or solar-type disk enclosed by a pair of wings. In ritual magic it is suspended over the alter in an easterly direction and used when invoking the protection and co-operation of the sylphs. 
A Masonic reference work describes it this way:
... the Winged-Disk, with the Uraei of Egypt, the original of which we find in the text summarized by Naville in the "Myths of Horus," pII. xii. ff.:&endash; "horus commanded Thoth that the Winged-Sun-Disk, with Uraei, should be brought into every sanctuary wherein he dwelt, and into every sanctuary of all the gods of the lands of the South and the North, and in Amentet, in order that they might drive away evil from therein...." This is what is meant by the Winged-Disks, with the Uraei, which are seen over the entrances of the courts of the temples of all the gods and goddesses of Egypt. 
Other occultic groups lay claim to the symbol and its use. A Rosicrucian reference work says this:
The Winged Globe is pre-eminently a Rosicrucian symbol, although the Illuminati may lay claim to it, and it may be admitted that it is of Egyptian origin. The Winged Globe is the symbol of the perfected soul making its flight back to the source of its creation in the Elysian fields beyond. 
This use of the symbol doesn't seem to relate to the Society's use of it in any recognizable way. Russell and Rutherford did not to my knowledge speak of perfected souls flying back to any "Elysian fields." Unless they were using it to symbolize flying back to the Pleiades upon their resurrection.
Where did Russell get this symbol then and what did it mean to him? Did he get it from Egyptian mythology? He was also clearly interested in the hidden, spiritual significance of the Great Pyramid of Egypt and spent much time discussing its importance. He also believed in a coming "Golden Age" which has its parallels with Egyptian mythology that also spoke of a coming Golden Age when the gods would come down and rule the earth and usher in a Paradise. This seems to be the extent of any parallels between the two.
The most likely source it appears to me would be his apparent involvement with Freemasonry. There is some evidence that Russell was a Mason and the Winged Sun-Disk, it is claimed, is a 330 Masonic symbol (The 33rd degree is the highest known level one can go in Masonry). The meaning of it is supposedly, like most other spiritual beliefs of this group kept secret by its members. If this is the source of his use of the symbol it may explain why he never explained why he started using it on his publications or what exactly it meant to him. It may have been a signal to other Masons.
However, based on his statements on the "Sun of Righteousness" mentioned in Malachi 4:2 we can get some idea of what it meant and symbolized to him.
The "Sun of Righteousness"
Russell apparently used the winged globe symbol to symbolize the coming New or Golden Age when righteousness would fill the earth and Paradise would be restored. Sickness and disease would end. Eternal life on earth would become possible for all those submitting to the beneficial rule of the 144,001 gods from the Pleiades.
This use of the symbol was evidently derived from Malachi 4:2 which says:
And to YOU who are in fear of my name the sun of righteousness will certainly shine forth, with healing in his wings; and YOU will actually go forth and paw the ground like fattened calves. (NWT)
Some view this "sun of righteousness" as alluding to the Egyptian winged-sun-disc symbol.
Russell and later the Society taught that the "Sun of Righteousness" here referred to the Millennial reign of "The Christ," head and body. These would rule earth from heaven in the Pleiades and "healing" would be in their "wings." They would help mankind become free of sin and disease. Given this, they could have viewed the "winged-disk" as a symbol of the coming Millennial reign of The Christ despite its connection with pagan religions.
However, during the Rutherford era they stopped using it because of this connection with Egyptian religion.
Satan and the Winged Disk
In 1921 the Golden Age published an article by Morton Edgar of Pyramidology fame (who they later would denounce for his involvement with pyramidology) on Egyptian mythology. In it he mentions the winged-sun-disk and its occult and pagan religious meanings. He wrote:
How rejoiced the poor groaning creation will be when Christ, the true "Sun of Righteousness," shall arise with healing in his wings. (Malachi 4:2) What a contrast to that cruel "sun" of unrighteous- ness, which arose with death in his wings. Malachi's allusion to the "wings" of the sun is evidently derived from the well-known symbol of the sun-god in Egypt and Assyria. Above the doors of the ancient temples and tombs in these countries, there is usually to be seen a representation of the sun-god, in the form of a round disc with wide-spread wings.
Along with the sun as the great fire-god, the serpent was connected. Owen says: "In the mythology of the primitive world, the serpent is universally the symbol of the sun". (Owen, apud Davies's Druids, in note, p. 437) In Egypt the commonest sign of the sun, or sun-god, is a disc with a serpent around it. (Bunsen, Hieroglyphics, Vol. 1, p. 497) The original reason for the connection of the serpent with the sun appears to have been that, as the physical world receives its light from the sun, so the serpent was held to have been the great enlightener of the spiritual world, by giving mankind the knowledge of good and evil. This, of course, like all idolatry, is an absolute perversion of the truth; but it serves to identify the sun-god with Satan. 
With this identification of the symbol with Satan the Society stopped putting it on its literature. Copies of the Studies in the Scriptures for example starting approximately at this time had a different cover design and did not have the symbol on it.
An Idolatrous Symbol?
In the Awake! magazine of December 22, 1976 the Society printed an article on idolatrous symbols. In the article they took a rare moderate position on the subject. They said the following after reviewing several images or "decorations" that have pagan religious roots:
With so many different designs having been used in false worship, if a person went to the trouble and took the time he might find an undesirable connection with almost every design he sees around him. But why do that? Would it not be needlessly upsetting? And is that the best use of one's time and attention? 
However, if the design or symbol had a clearly understood idolatrous (false religious) meaning, Christians were to avoid it:
If a particular design or shape is commonly understood where you live to be a religious symbol, there is good reason to avoid it. 
One of these religious symbols connected with a pagan god mentioned and illustrated in the article was of the "Winged Disk" of Egypt.
So What's the Big Deal?
What is the significance of Russell's introducing without explanation the Winged-Sun-Disk on his publications? This depends on what significance it had for him. I have not been able to pin down to my own satisfaction exactly, or even roughly, what it meant other than perhaps a symbol of the coming Golden Age. That the symbol has various occult and religious meanings is apparent, but what did any of these have to do with Russell's use of it? If Russell was a Mason and used it because of this, what would this mean? This would depend on what, exactly, it means or symbolizes to 330 Masons. This is hard for me to ascertain.
Rutherford put an end to its use by the Bible Students because of some of these occult (Satanic they would say) connections. This was a move in the right direction it appears to me as I can't think of a legitimate use of it for Christians.
Other Masonic Symbols
Other Masonic symbols adorned early Watchtower Society literature. The most famous of these is the "Cross and Crown" symbol. This is supposedly the Knights Templar logo in Freemasonry.  It has also been used by numerous other groups and individuals, many of which (such as the Theosophists) are associated with the occult but others are regarded as Christians.
Another symbol is the so-called Knights of Malta symbol. This was put on the cover of the Watch Tower in the upper right hand corner opposite the Knights Templar logo. 
There are other symbols as well used by Russell that have Masonic origins. Again, what significance does this have? How much was Masonry an influence on Russell? Does it matter anyway? Given the secret nature of the group and Russell's silence on the matter, I can't determine the significance to my satisfaction. The secrecy and misinformation on the part of Masons has led to speculation and incredible conspiracy theories. 
Footnotes and references:
1. Hope, Murry, Practical Egyptian Magic (New York: St. Martin's Press), 1984 p. 107. Quoted by Fritz Springmeier, The Watchtower & the Masons, 1990, 1992 pp. 113, 114.
2. Churchwald, Albert, The Signs and Symbols of Primordial Man,... (London: George Allen & Co., Ltd.) 1913 p. 344. From a photo copy in Springmeier, p. 114.
3. Swinburne, Clymer, The Rosicrucians Their Teachings (Quakertown, PA.: The Philosophical Pub. Co.), 1923 p. 112. Quoted by Springmeier, p. 115.
4. The Golden Age, May 25, 1921 p. 506.
5. Awake!, Dec. 22, 1976 p. 15.
7. Springmeier, Fritz, The Watchtower and the Masons, 1990, 1992 pp. 71-110.
8. Ibid., pp. 88, 95. Fritz does not offer any documentation that this symbol was the same as the one on the Watch Tower's cover however.
9. The Watchtower and the Masons suffers from this. To illustrate the secrecy of Freemasonry, I have one Masonic book in my library that is completely written in symbols and abbreviations. I can not make heads or tails of it. The book does have a stern warning in plain English about copyright laws and says "This book is restricted to the use of Master Masons ONLY in good standing. It is neither to be sold nor loaned to any other." It is enclosed in a plain blue case of sorts that snaps shut.