I've never seen this marking on a watch fob before. It is quite worn, so some of the lettering is unreadable. Overall width is 29 mm or 1 1/8"
Can anyone give us some information about the history of this organization and when they were active?

ED,
A goggle search turned up these:

http://americanhistory.si.edu/onthemove/collection/object_188.html

http://en.wikipedia.org/wiki/American_Federation_of_Labor

Looks like it was part of the AFL who later merged with the CIO.

Founded by Samuel Gomphers and tried to recruit workers from all the brotherhood unions under one umbrella.

I found this as part of this site:
http://www.marxists.org/archive/foster/1921/rrns.htm

This was written in 1921, and apparently the A F of RR W was still in existance at that time.

The American Federation of Railroad Workers occupies a unique position among the many dual industrial unions that have sprung up from time to time on the railroads. While all the others have been radical, it is markedly conservative. It has had a checkered history. Originally it was the International Association of Car Workers, an A. F. of L. union. But as there was a conflict in jurisdiction between it and the Brotherhood Railway Carmen of America, the A. F. of L. ordered the two bodies to amalgamate. The president of the I. A. of C. W. refused point blank to agree to this salutary measure, and surrendered his charter to the A. F. of L. at the Atlanta Convention in 1911. The organization struggled along for a few years as a craft union, and then, in 1915, it extended its jurisdiction to take in all railroad workers, calling itself thereafter the American Federation of Railroad Workers. Its membership at the present time is estimated to be about 9000, principally car workers. It has contracts on two or three railroads.
From its inception the A. F. of R. W. has been a thorn in the side of the old unions. It has done them much harm, to the glee of the companies. Its latest exploit is a clear betrayal of the great masses of workers on the roads. Just now, when the other unions are fighting to retain the national agreements, so that the gains of the past few years will not be lost, the officials of the A. F. of R. W. step in and sign an agreement with the Philadelphia & Reading, which not only gives up the principle of the shopmen’s national agreement altogether, but also many of the conditions established by the same. But such are the fruits of dual unionism generally, no matter in the name of what high-sounding principle the rival organization operates.

Here is a charter from the American Federation of Railroad Workers. It was issued to Lodge 46 located at Delanson, New York on the Sixteenth day of February in the year of Nineteen Hundred and Fifteen

Delanson was part of the Albany and Susquehanna Railroad that was built from Albany to Binghamton, New York the railroad was leased by the Delaware and Hudson Railroad, and a line was built from Delanson to Schenectady there were shop facilities the name of the town Delanson was derived from the D & H using the first three letters of Delaware, the first two letters an from and, and son from the last three letters of Hudson

The calligraphy on the charter looks like the watch fob