I have been taking various training tests and the answer almost always involves some sort of forcing move. Clearly attacking a king will always force a response but when another piece is involved (whether it be major or minor) an attack does not need to be forcing. Are there rules of thumb to help identify forces in these cases? I tend to look for mates, royal forks followed by forks and then winning exchanges. Where I stumble is if a test involves a forcing attack that leads to mate. I always just assume I would sacrifice the piece to stay alive.
Forcing move is a term for a move that leaves an opponent with a few options, only one of which does not lead to an immediate loss. This could refer to a variety of circumstances. For example, you might see a mate in 3 puzzle in which the first move is a forcing move because the opponent's only other legal move falls to a mate in 1. The term can also be used in opening theory, like in Ruy Lopez situations where black's b5 forces Bb3, or the loss of the bishop. The term may also be used for situations like 1.e4 c5 2. Nf3 Nc6 3. Bb5 a6, after which white is left with one good option, 4. Bxc6, and several bad options, such as 4. Ba4, which just loses the bishop, 4. Bc4, which allows black queenside expansion while losing another move, 4. Bd3, which blocks the d-pawn, 4. Be2 which is probably the best alternative but yields the b5 square without a fight, and 4. Bf1, which severely hampers development. While white has other options, they are strategically weak, and it could be said that black's a6 is a forcing move. So there is a wide spectrum between checkmate situations and less dramatic situations in which there is only one reasonable move.
In the context of your training tests, some positions may require identifying some weakness, and then exchanging or driving off the most important defender by coming up with a "forcing move". You are often advised to begin your thinking by looking for forcing moves, but not every forcing move is good. When you find one, ask yourself what it positively achieves. Another plan is to begin by seeking the weakness, and then looking for forcing moves that relate to it.