It is difficult to craft the definition of elderly, as it is interpreted differently by people. In America (as well as other cultures & countries), there is a stigma attached to being old, which informs the view that many have on the word.
In general terms, many of the developed countries have accepted age 65 to represent the age at which one becomes elderly. This may have been due to the fact that earlier in our history this was the age that people could begin collecting retirement benefits.