Can someone explain this analysis to me?

When I click on "show idea," my rook is returned to where it was and my pawn advances. Their bishop immediately captures my pawn. My understanding of a "passed pawn" is a pawn that can advance to the back rank and be promoted. What am I missing here?

A pawn being "passed" doesn't necessarily mean it can be promoted. It means that no other pawns can potentially capture or block it, and as a result the opponent's pieces must work to stop it. By moving the pawn forward, all of Black's pawns are either behind it or too far away, making it "passed."

I believe the reason d6+ is the best move isn't because it passes the pawn, though. Obviously, that move dooms your pawn. However, it does clear the diagonal your light-squared bishop is pointing at, making it much more active than it was before. That, and you could get rid of Black's dark-squared bishop, which would have had a high potential to be somewhat problematic if it were to go to b6.

h3 also looks like a good move, as it would force the black knight to retreat to a quite passive square in the corner and further congest Black's already poor positions. It would also allow you to play Bf3 safely, allowing your other bishop to become a bit more active as well. You could even play Ng5 afterward, threatening a crushing skewer (Bxg5+) if they take the "free" knight (assuming you didn't play d6+ first), and allowing the knight to go to the powerful e6 square if they don't.

Re1 isn't really a "terrible" move, but the problem is that the rook is still hardly doing anything on that square, so it's effectively a waste of tempo.

This is why computers make bad teachers. They can show you what the "best" move is, but their ability to explain why that move is so good leaves a lot to be desired. In this case, labelling the idea "Passed Pawn" is unhelpful to a human who is trying to understand why one move is better than the other.

Firstly, to clear up any confusion on the technical side of what happens when you click "show idea": The reason your rook goes back where it was, and the pawn advances, is that the computer is showing you what the position looks like IF you had made the move it is saying you should have made, instead of the one you did make.

A "passed pawn" is a pawn that cannot be captured or blocked by an enemy pawn on its way to promotion - that is to say, there are no pawns ahead of it on the file it is on, or the files either side of it. That doesn't mean it can't be taken by other pieces. So, once the pawn advances to d6, it is technically a passed pawn - even though it will be immediately taken. Even so, it is unhelpful for the computer to say "show idea: Passed Pawn", because the fact that it will be a passed pawn for as long as it takes Black to make their move does nothing to explain why you should make that move.

The reason d6 is the best move is that you are losing the pawn anyway, but how you lose it matters. Black is threatening cxd5, which will kick your knight. In turn, you lose a good square for your knight, and Black gets more mobility. Moreover, after Black plays Bxd6, you will have the option of exchanging off your e4 knight for the d6 bishop, which could be a strategic advantage for you, as you will have the "bishop pair". Bishops can be more effective when both of them are on the board. So the idea here is mobility and piece harmony, rather than "passed pawn". But the computer struggles to explain that. Hope this helps

Yes. The engine giving false or misleading information is a real problem.

For example, it once told me I "missed" an opportunity to threaten checkmate, when the move I played did exactly that.

I've also had it say the following:

- "You get the chance to eventually win a bishop." (The bishop was straight up hanging and could be taken on the very next move, so it wasn't "eventual" at all.)

- "This allows you to capture a knight and win material after the follow-up trades." (The trade was winning a bishop. The knight they were talking about had absolutely nothing to do with the trade.)

- "Nice fork! You'll win a rook." (The move was forking a rook and a knight. Why would my opponent not move the rook? Also, when my opponent did move the rook, it said it was a mistake because they "left" the doomed knight hanging.)

This a generalization. The problem isn't with "computers" in general. The problem is with chess.com's dumb Game Review software which is ridiculously bad. Talking about a "passed pawn" in this position is insane. I can't fathom how people are willing to pay for that complete nonsense.

If you switch to Analysis, the chess engine shows you what is going on. Move by move, as deep as you wish.