The term thermae was the word used by ancient Romans for the buildings housing their public baths.
Most Roman cities had at least one, if not many, as such buildings that were centers of public bathing and socialization. Upper-class Romans will normally visit daily, lower-class people about once a week.

Building Layout

Within the building the baths were then divided according to gender. Each gender had three pools: a hot one, a lukewarm one and then a cool one. They were respectively called:

The Caldarium
The Tepidarium
The Frigidarium

Sometimes there was a steam bath: the sudatorium.

Thermae Bath SpaCaldarium from Roman Baths at Bath, England. The floor tiles have been removed to expose empty space through which hot exhaust gases flowed, heating the tiles.

The baths normally included, aside from the three main rooms, listed above, a palaestra, or even outdoor gymnasium where men may engage in various ball games and exercises. There, inter alia, weights were lifted and sometime discus thrown.
Men would oil themselves (as soap was still a great luxury good and thus not widely available) and removes the glut with a strigil (c.f. the well known Apoxyomenus of Lysippus from the Vatican Museum).

The changing room was known as the apotyterium.