Six moves into an Italian, Black plays Bb4 and the bishop stares down the a5-e1 diagonal at the white king. That is check. Nothing has been won, nobody is getting mated, the position is dead level. But White’s next move has stopped being a free choice: of the thirty-odd moves that existed a second ago, only the ones that deal with that bishop are legal.
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e h 1 Check is one thing and one thing only: an enemy piece attacks the square your king is standing on. Article 3.9 of the FIDE Laws says it in a sentence, and adds the detail players argue about, that a piece gives check even when it is pinned and could not legally go to that square. The attack is answered on this move. Not the next one.
Three answers, and only three
Capture the piece that is giving check. Block the line between it and your king. Move the king to a square nothing attacks.
That is the whole list, and it pays to run through it in that order every time, because beginners see the third answer first and grab the king before they notice the checking piece was hanging. In the diagram White has five blocks (7.Nc3, 7.Nbd2, 7.Nfd2, 7.Bd2, 7.Qd2) and two king moves. Nobody plays a king move. 7.Kf1 is perfectly legal and perfectly horrible: castling is gone for good and the rook on h1 sleeps for the next twenty moves.
Two of the three answers vanish more often than you would think. You can never block a knight check, because the knight jumps and there is no square in between to stand on. You can never block a check from a piece that is already touching your king. And you cannot capture a checking piece that is defended, at least not with the king. Getting out of check walks the whole checklist with a board in front of you.
Sometimes there is exactly one legal move
7 2 g Count Black’s replies in that picture. He cannot block, because knights are not blockable. He cannot take the knight, because no black piece attacks e7. Of the eight squares around his king, three are off the board and four are occupied by his own men. That leaves h8. So Kh8, and that is the entire set of legal moves available to a player with a rook, three pawns and a king.
This is the thing to understand about check, and it is the reason tactics work at all. Check strips the position down. It takes a wide, murky middlegame and turns it into a corridor, and the whole art of a combination is walking your opponent down that corridor while you help yourself to material behind his back. When the number of legal answers hits zero, it is checkmate and the game is over.
What you are not allowed to do
You cannot ignore it. Playing a developing move while your king is attacked is not a weak move, it is not a move: the position gets put back and something happens to your clock if there is an arbiter in the room.
You cannot step onto an attacked square, in check or out of it. Kings are the only pieces with squares they are forbidden to visit.
You cannot open a line to your own king either. A knight sitting between your king on g1 and an enemy bishop on a7 is welded there; it can be attacked, kicked and offered a free queen, and it still cannot move. That knight is pinned, and a pinned piece still gives check in the other direction, which surprises people every time.
Discovered check, double check, and the + sign
A piece slides off a line, and the rook, bishop or queen sitting behind it is suddenly attacking the king. The checking piece is the one that never moved. What makes it brutal is that the piece which did move is free to go anywhere at all, including somewhere it could be taken, because the opponent has to answer the check first and by then it is too late. Even a king can do the uncovering, which is the one way a king takes part in giving check.
When the moving piece gives check as well, both at once, that is double check, and it cuts the list of three answers down to one. You cannot capture two attackers with one move and you cannot block two lines with one piece, so the king must move, full stop. The classic smothered mate is built on exactly that: the knight drops into h6 with double check, the king has to go to h8, and then the queen comes to g8 to be captured. Puzzles on both are here: double check and discovered attack.
Written moves mark check with a + on the end: 7…Bxd2+. Mate gets a # instead, and many writers use ++ when the check is a double one. There is more on what + means in notation, and no, you do not have to announce anything out loud.
The habit that saves the most rating points is a dull one. Every time your opponent moves, before you think about your own plan, ask what that piece now attacks and whether your king is on the list. Most beginners who hang a queen were not outplayed, they were in check and did not look, which is half the subject of how to stop blundering.