Elgin, or more correctly the Elgin National Watch company, was a maker of fine pocket and wristwatches. It was founded in 1864, and produced their first watch in 1867 (an 18 size railroad watch). They continued to make watches until the 1960's, when they got out of the horology business and became Elgin National Industries (www.eni.com).
Elgin, and their competitor Waltham, dominated the middle ground of pocket and wristwatches. Both comapany's watches are fairly popular on the used market, as they can be worn every day and aren't too expensive, due to the volume of watches that were produced.
I'm currently wearing a Lord Elgin 25 jewel selfwinding wristwatch. I think it's around 50 years old, at least. Still keeps correct time, without the need for batteries.