A ko threat is a move with a "big" follow-up, which you play after your opponent has captured a ko; if your opponent answers it you may recapture the ko. (You cannot recapture the ko immediately, due to the basic rule of ko.) If your opponent does not answer your ko threat, but instead proceeds to resolve the ko, you can follow through on your threat and thus gain compensation for losing the ko.
The basic sequence of a ko fight is thus (1) White takes ko (2) Black makes threat (3) White answers threat (4) Black takes ko (5) White makes threat (6) Black answers threat (7) White takes ko, and so on until finally (3n) Black or White ignores threat to resolve the ko (3n+1) White or Black follows up on threat.
The term ko threat can be used to refer to a potential threat as well as one actually played. Example: "White has more ko threats than Black."
The term "ko material" is an alternative to ko threat, which can also refer to the aggregate of all potential ko threats one player has, as in "Felix has more ko material than Oscar." The Japanese terms kouzai and koudate, do not distinguish between singular and plural, and thus may be used to refer either to ko material in the aggregate or an individual ko threat.
The "size" of a ko threat is, informally, the potential gain from making the threatened follow-up (when your opponent ignores the threat and instead resolves the ko).
Ko is a Japanese go term adopted into English usage. It describes a situation where two alternating single stone captures would repeat the original board position. The alternating captures could repeat indefinitely, preventing the game from ending. The ko rule resolves the situation.