In the game of
Go (
Wei Qi/
Badouk), territory means empty points fenced in by one player's stones (and possibly edges of the board). Basically, whoever has more territory at the end of the game wins (although any stones of the opponent's that you
capture get added to your score as well).
Officially, territory is only determined after the game has ended. However, it is common to refer to an area as one player's territory if it is pretty much guaranteed to still be his (or her) territory at the end of the game. Here is a diagram to illustrate (edge of the goban marked by ###):
#............
#............
#..x.........
#..ox........
#::ox........
#::o.........
#:::oxx....x.
#:::oox......
#::::........
#############
All the points marked with : would be considered White (o) territory, because there is no way for Black (x) to invade or reduce it. At the end of the game, it will still belong to White. It would be incorrect, however, to call the points to the right Black's territory at this stage, because, although Black will likely get some or all of it, there are still possibilities for White to deny Black territory in that area. Instead, the correct thing to say is that Black has a lot of influence over that area (see my influence writeup for more info).