It is a fairly common variety of "faux" (false) US Navy button made for use on civilian imitation Navy PEA coats (and some other foul-weather coats). Note that your button's emblem has very weak "detail" (not sharply detailed like the actual US Navy button in the photo below, and it has 7 stars instead of 13, the eagle has round-topped wings, and the anchor lays horizontally but is vertically on its edge (instead of the "stock" (the crossbar) laying sideways like on the actual US Navy button, shown below.
Another clue that it is a cheap civilian-usage imitation of an actual Military button is the fact that (like most such buttons) it had a thin iron/steel back which has rusted out.