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:
[FEN ""] 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.
The definition is opinion based. A solid line makes me feel a line which is less complicated, the variants are known and more analyzed before. Opening books are certain about them and a transition from opening level to the middle game is played many times before in GMs games. A solid line probably needs less reminding efforts at the game and the main line is clear to discover. Also there're a few traps in solid lines.
On the other hand, a critical line is a line which is not analyzed comprehensively, it has many unknown variants and a simple mistake leads to lose the game (if the opponent also catch the chance). If someone doesn't follow the main line, it's hard to discover the best moves in the game.
I doubt that there is any type of official definition for these terms. It seems to me that a "critical variation" simply leads to positions where your opponent has more active play, and where it is easy to make mistakes, whereas a "solid variation" is one where you have more active play, and your opponent has to play carefully to avoid making mistakes.