Aji - a potential. some weakness to be exploited

Atari - danger of immediate capture (stone or a group has only one liberty)

Dame - a neutral point not surrounded by either player

DDK (double digit kyu) - a player below 9k

Geta - a net

Gote - an opposite of sente, playing a move that does not need to be answered

Joseki - a known sequence (usually near a corner) that is believed to be optimal for both

SDK (single digit kyu) - a player stronger than 10k but weaker than dan.

Sente (initiative) - a state where you do not feel the need to respond locally and chose where to play next

Tesuji (clever play) - a local move that usually beautifully solves some trouble, without any chance of being foiled

For more look here: Common terms
For even more look here: All terms