Sometimes in chess you do whatever you want to do and then your opponent does whatever he wants to do. Other times it’s different: if you capture his knight with your bishop, for example, he pretty much has to recapture your bishop; otherwise he simply is short a piece and probably will lose. (The other pieces belonging to both sides gradually will be exchanged away, and you will end up with the only attacking piece left on the board.)
Another example: If you check your opponent’s king, he can’t do whatever he wants in reply; he has to either move the king, block the check, or capture the piece you have used to make the threat. And if you make a move that will enable you to deliver checkmate on your next turn—a “mating threat”—your opponent likewise will have to address it immediately.
Checks, captures, and mate threats therefore are known as forcing moves. In other words, they are moves that force your opponent to pick from a small set of possible replies. They are the essence of tactical chess; they allow you to dictate your opponent’s moves and thus control how the board will look two or three or more moves from now. Other types of moves may be "forcing" as well, mind you: any threat you make against your opponent—for example, a simple threat to take one of his pieces on your next move—may force him to reply in a certain way. This happens all the time, and we will see examples as we go. But checks, captures, and mate threats tend to be the most interesting and important kind of forcing moves because they so powerfully limit your opponent's choice of replies.
This notion of forcing moves helps clear up some common confusions about chess. No doubt you have heard about good players seeing ahead five moves, or a dozen moves, or more; how do they do that when their opponents have so many possible responses to pick from? The usual answer is that their opponents don’t have so many choices after all. Suppose I think like this: if I take your knight with my bishop, you will have to recapture my bishop; then if I check your king, you will have to move it over one square; then if I check your king on its new square, you will have to block my check; then your rook will be left loose and I will take it. In this case I have seen ahead four moves, but notice that I didn’t have to keep track of a lot of possible variations. To each of my moves you only had one plausible reply. I just had to realize this. Of course sometimes your opponent will have more than one plausible reply, and in that case you will need to keep track of some variations after all (“if he does this, I’ll do that; if he does the other thing, then I go to plan B,” etc.). And it’s true that very strong players can keep straight lots of variations. But it’s also true that a lot of great tactical sequences consist entirely of forced moves that make it not so hard to see ahead.
Once you grasp the idea of forcing moves it also is easier to understand how to come up with nifty tactical ideas during your games. Of course you might like to unleash a fork or discovery or skewer, but what if no such moves are possible when it’s your turn? Do you wait around for a fork to become available? No; your first job when you are deciding what move to play is to examine your possible forcing moves: any checks, captures, or mating threats you can offer. You don't look at these things just as ends in themselves; you ask what moves your opponent would be forced to make in reply, and whether you then would be able to play a fork or discovery or skewer or some other tactic. If the answer is no, you imagine playing another forcing move after the first one and then ask the same questions.
The point of experimenting with forcing moves, in short, is that they change the look of the board. They may open up lines that currently are cluttered; they may cause your opponent to leave pieces loose that now have protection; they may make him line up pieces that are not now on the same line; they may make him put his king where it can be checked. Your task is to imagine the board as it would look after your forcing moves and see if changes such as those would create tactical openings for you. Gradually a pattern you recognize may emerge—the makings of a fork or discovery or other idea.
With practice this becomes second nature: if your rook is aimed at your opponent’s knight, you automatically consider capturing the knight and allowing your rook to be taken. This would be a sacrifice, of course, since rooks are more valuable than knights, but great tactical ideas routinely begin with sacrifices like that. The question is whether the exchange of your rook for his knight would leave you with a chance to play a fork or other double threat—or with a chance to play another forcing move that isn’t yet possible. Maybe after your rook is captured you then can play a check that wasn’t available before; and maybe after your opponent responds to the check you then will have a fork. But it all starts by thinking about a simple capture you can make and its consequences.
Likewise, you generally don’t want to make any moves without being aware of any checks you give and their consequences. Checks are the most forcing moves of all because your opponent is required to reply by moving his king, taking the piece that threatens it, or moving a piece between them. This usually makes it easy to see what a check will require your opponent to do. And since a check often forces your opponent to move his king, it may lead directly to tactics that make the king a target—a fork with the king at one end, or a pin with a king at the rear, or for that matter checkmate.
Looking at any checks and captures you have to offer is like looking for loose pieces on the board: these are things you do all the time during a game, because most great tactical ideas involve one of those elements or the other.