Damas means "ladies" or "dames". It's a bit old-fashioned. You'll find it in the stock phrase "damas y caballeros" ("ladies and gentlemen"), but this kind of thing is on its way out. You'll also see damas as a label for bathrooms. You can often substitute señoras. Unlike señora(s), you cannot use dama(s) as a vocative (i.e. to call or address someone) by itself.
Damas is also the name of the game of checkers. Dama is also one of the names (besides reina) for the queen in the game of chess. The pieces of checkers were originally named in French fierges, the same as the chess queen (for Persian ferz "vizier"); when the queen changed its name to dame the checkers pieces took it as well.