Brinkmate is the situation in which an unavoidable checkmate sequence will be created by the player's next move.
In shogi, brinkmate is known as hisshi (必至 "desperation, inevitability" or 必死 "sure kill"). Note that in shogi tsume is defined as strictly forced mate sequences with constant checks. The checkmating sequence itself (after the brinkmate) is known as a 詰め tsume.
Brinkmate differs from the situation in which a checkmate sequence is only being threatened to be created in the next move but is still avoidable if the opponent defends correctly. This situation is known as threatmate or, in Japanese, 詰めろ tsumero ("threatened mate"). Thus, brinkmate is an indefensible threatmate.
The only way to prevent a loss from a brinkmate is for the defender to not give their opponent a chance to actually create the checkmate sequence and instead initiate their own mating sequence (with constant checks) before their opponent's move. (Thus, a good exemplification of the saying the best defense is a good offense.)
Some brinkmates involve tsumes that needs two condition to be met in order to defend (e.g. two mates are threatened). The defending side could give a check and simultaneously meet one condition (which is only possible in shogi games and brinkmate problems involving two kings), and then satisfy the other condition.
Although the terms brinkmate and threatmate were coined to translate the Japanese terms in shogi, the concepts can equally be applied to western chess and other chess-like games. (See: §Western chess below.)
In xiangqi, threatmate (催殺 "to expedite mating", often abbreviated as 殺) and brinkmate (絕殺 "absolute (indefensible) threatmate") are also common terms.