The cannon
The piece with no chess equivalent, and three things its screen does
Updated
A cannon moves like a chariot, along a file or a rank over empty points. It captures differently: it must jump over exactly one piece — the screen, of either colour — and take the first enemy piece beyond it. No screen, no capture; two pieces in the way, no capture. The rule is on the rules page, and two attacks built on it are on the middlegame page. This page is about what the screen does that no chess piece can.
Every cannon attack has a weak point
A chess rook's attack depends only on the line between it and its target. A cannon's depends on that line holding exactly one piece. That makes the screen part of the attack: take it away and the attack stops, and add a second piece and it stops too. Both are moves the defender can make, and neither has any counterpart in chess.
Two extra answers to a cannon check
A general in check from a cannon can step aside or have the cannon taken, as with any check. It has two more answers: move the screen off the line, or put a second piece on it.
So the first question when a cannon checks you is not "where can my general go" but "what is its screen". If the screen is yours, moving it is a free answer, and it may even move somewhere useful.
You may not step between a cannon and your general
The same rule works the other way, and this is the part that catches people. If an enemy cannon faces your general down an empty line, it is not giving check — there is no screen. So nothing of yours may step onto that line, because the piece that steps there would become the screen, and you may never make a move that leaves your own general in check.
The practical version: a cannon aimed down an empty file at the general is quietly taking that file away from the defenders. Nothing of theirs can cross it without walking into check.
Two cannons on one file
Put two cannons on the same file, one behind the other, facing the general with nothing else between. The front cannon has no screen and gives no check. The back cannon uses the front one as its screen and does. This is the double cannon, 重炮.
What makes the double cannon so hard to meet is that the usual interposition does not work. Against one cannon, a second piece between it and the general is a defence. Against two, a piece between the general and the front cannon turns the front cannon on, so the check never goes away — it just changes which cannon is giving it. The one square where a blocker does work is between the two cannons: with them on e5 and e7, a black chariot that can reach e6 has the only legal reply, and the same chariot able to reach only e4 has none.
What to do with it in a game
When a cannon checks you, look at its screen before your general. Moving the screen away, if it is yours, costs nothing and often develops a piece.
Treat a cannon on an open line to your general as a wall. It is not check, but it decides where your defenders may stand, and one more enemy piece arriving on that line turns it into check.
Never let two enemy cannons line up on your general's file. Against one, anything that can reach the line in front of your general is a defence. Against two, only a piece dropped between the cannons is, and when they stand next to each other, as in the diagram, there is no such square.