Atari

Sensei's Go Terms defines atari as "the state of a stone or group of stones that has only one liberty."

This means that it (or they) are only one move away from being captured.

DIAGRAM 1

In Diagram 1, reading from left to right:

(1-4) The stone 1 is "in atari" and can be captured if black plays d3.
(5-16) The stones 2-4 are "in atari" and can be captured if black plays i3.
(5-16) The stone 5 is "in atari" and can be captured if black plays m1.
(5-16) The stone 6 is "in atari" and can be captured if black plays s2.

Some people say "under atari": it means the same. Some players - particularly begiinners, and people playing with beginners - will announce "Atari" like some players will announce "Check" in Chess. It's a courtesy, but don't expect it. It won't happen in higher levels of play.