It means both. You should fasten your seatbelt when you first sit down, and you should keep it fastened at all times in which you are in your seat (the only time in which it should not be fastened is if you're not in your seat).

Scott--when they turn off the fasten seatbelt sign, it's usually just an indication that you're allowed to get up out of your seat to stretch or use the lavatory. They usually want you to keep it fastened while you're in your seat even after they turn the light off.