This recreation of a Roman villa, designed by Shaun Venish (who also did the amazing interactive map of Rome, not to mention the logo on my History Buff blog!) shows the various parts of a typical Roman villa during the age of Augustus.
Triclinium: the dining room in a Roman household, so named for the three couches on which diners reclined and ate.
Atrium: an open area in the center of many Roman homes.
Tablinium: A room used as the formal reception room, living room or office by the head of the household.