Explanation

Sometimes you can capture an opponent's piece, but capturing it comes with a disadvantage, for example, your opponent may have other threats, or the piece that can make the capture may currently be pinned. In those cases, instead of capturing immediately, you can sometimes play an intermediate check - a move that gives check and changes the situation so that you can make the capture later without that disadvantage. Here are some examples:

In the first diagram, the white rook is attacking the black knight, but the black rook is attacking the white queen. White can solve this garbage collection with the intermediate check indicated by the arrow. With the queen on a safe square, White can then capture the knight on the next move: 1.Qd4+ Kc7 2.Rxa8.

In the second diagram, the white rook could capture the black knight, but it is pinned by the black rook. White can give the intermediate check indicated by the arrow to move the queen out of the pin; White can then capture the knight on the next move: 1.Qd5+ Kc7 2.Rxa5.

In the third diagram, the rook is again pinned. There is no intermediate check with the queen, but the knight can give the intermediate check indicated by the arrow, forking the king and bishop. White can then capture the bishop on the next move with the knight: 1.Nb7+ Kc7 2.Nxa5.

In these levels we are looking at intermediate checks to avoid losing material to a capture or trade.

Examples

Black has just captured your queen with Qxb3. Do you recapture?
Not immediately, because the queen capture has also discovered an attack of Black's roon on e8 on your unprotected rook on e5.
If you blindly recapture with 1.axb3?, you would lose that rook to 1...Rxe5.
Instead of recapturing immediately, you can first exchange rooks with the intermediate check 1.Rxe8+!
After black recaptures with 1...Rxe8, you can capture the queen with 2.axb3.

Black has just captured your bishop on e5 with Bxe5.
Recapturing immediately is not a good idea, because the rook on c7 is now unprotected.
After 1.dxe5?, Black could win that rook with 1...Qxc7.
Instead of recapturing immediately, White can play the intermediate check 2.Qxe6+.
After the king moves out of the check, White can capture the bishop with the queen, which also protects the rook on c7, for example 1...Kh8 2.Qxe5.
White has won a pawn instead of losing a rook, and is now a pawn up in the endgame.

How to spot an intermediate check

When you can capture an opponent's piece, don't just grab it. Instead:

1. Look for existing threats from your opponent.
2. Consider whether your intended move might create tactical opportunities for your opponent.

If either of these exist, consider an intermediate check or move.

Related motifs

An intermediate check is an intermediate move which is a check. An intermediate move can sometimes be a counter attack, and intermediate check is always a counter attack on the king.