Explanation

Sometimes you can capture an opponent's piece, but capturing it comes with a disadvantage, for example if your opponent has other threats, or if the piece which can make the capture is currently pinned. An intermediate check is a move giving check that you play instead, which changes the situation so that you can make the capture later without that disadvantage.

In these levels we are looking at intermediate checks to avoid checkmates.

In level 1, we make two moves, and avoid a checkmate in one.
In level 2, we either make three moves to avoid a checkmate in one, or we make two moves to avoid a checkmate in two.

Examples

Capturing the rook with 1...Rxb2? would not be a good idea, because of 2.Qxd8#.
But black can win with the intermediate check 1...Rd1+. After the forced 2.Kh2, Black can now capture with the other rook 2...Rxb2, while the rook on d1 is still protecting the knight on d8.

Sometimes the intermediate check can be a sacrifice:

It would be a mistake to capture the queen immediately with 1...Qxg4, because Nb6# would be checkmate. Instead, Black can win with the intermediate check 1...Rd1+!, sacrificing the rook to deflect the rook from c1. After the forced recapture 2.Rxd1 Black can capture the queen without being checkmated.

Capturing the queen immediately with 1.Qxa7? fails to 1...Rxc1#.
However, White can play the intermediate check 1.Rd8+!.
If Black captures the rook with 1...Rxd8!, then after 2.Qxa7 there is no checkmate.
And if Black defends with 1...Nf8, White wins with 2.Rxc8.

Visualization

When you can capture an opponent's piece, don't just grab it. Make sure that your opponent doesn't have any threats. Those threats can exist before your move, or only after your move. If such threats exist, consider an intermediate move or check.

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