What is a critical variation? Sometimes I hear that a critical variation in a certain opening was avoided and instead a solid variation was chosen. Can someone explain to me what a critical variation is? Maybe also explaing in the process what a solid variation is?
A critical variation is one that the evaluation of the current position depends on.

Take the Morra gambit:

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1.e4 c5 2.d4 cxd4 3.c3


Is the Morra gambit a correct opening, or has white made a mistake? It does sacrifice a pawn, so the evaluation probably depends on whether white gets enough compensation after 3...dxc3. So that is the critical move. It's also the riskiest, because white does get some open lines and development, so he can probably at least set up some threats in the short term.

3...d3 is another move, declining the gambit. White doesn't get quite as quick development, but he's not a pawn down either. After this it's likely that the position is more or less equal, and it's just a game of chess. This is a move to play if you want to avoid risk, but it's not the place to look for a refutation of the Morra. So it's not critical.

A solid move is the oppositie of a risky move.