Bc4 has gone out of fashion in over the board play in a sicilian, but for some reason still seems quite present here on gameknot. It isn't that popular anymore since quite a few mastergames have shown that after something like e6 -> Nc6 -> d5 black reaches equality rather easily. I like the concept of Bc4 since it strikes at a weak point and it can draw sicilian players who prefer d6 variations such as the najdorf into e6 variations that they might not know as well, but it seems a tiny bit too weak in my opinion.

Though this is a good move after 1...e5, it is less good here, for two reasons: [1]: the Black e-pawn not yet moved can (and will) play to e6 to block the strike against f7; [2]: The bishop now stands as a target, accelerating Black's thematic Q-side expansion by ...a6 and ...b5. These aren't fatal downsides by any means, but usually one prefers to cede nothing to one's opponent.

I did say "good" rather than "best"! Bipolarcorner is right to say this move is popular on Gameknot - in fact the 3rd most popular move after Nf3 and Nc3. Nf3 is what I would play.

But see how the White bishop provides the motive for Black's moves already.

Was d5 at once possible? It seems so...

d5 is usually delayed damalfi, jkarp. The reason for this being that d5 allows a weakness on the a4 - e8 diagonal and invites a check from white's bishop. It's a small nuance, since black will still be attain center control, but it's not too difficult to challenge that center control for white. The usual response to an immediate d5 is something along the lines of 3. d5 4. Bb5+ Nc6 ( Black's light squared bishop usually tends to be more important then white's in the Bc4 sicilian so although Bd7 is a possiblity, Nc6 is better ) 5.exd5 exd5 after which white can castle, and quickly bring his pieces out as compensation.

Yes I could have played d5 immediately, but then he can check with the bishop on b5.

She avoids the 'Noah's Ark' type of trap: 5.Bb3?? c4. White can still show a lead in piece mobilization, but Black is happy to have with pawns staked out already the territory he wants, within which his development will be rapid enough.

Gaining more time.

Developing the bishop to a natural square of several e6 sicilians in the process.

A classic theme in a lot of chess puzzles: removing the defender. Here in Belgium we follow a 6 "stepsystem" if you're young and go to a chessclub. They teach you this type of stuff when you reach step 3/4 through a variaty of puzzles.

Short range oversights happen to us all, but they do get rarer with experience, knowledge, and - let's face it - advanced ratings. Of course their becoming rarer helps advance those ratings! But certain types of oversight always surprise me. White knows full well that the f8-bishop has a line to c5, yet forgets about it momentarily in the face of the loss of a pawn.

Black has now a winning game - an extra minor piece, more space, more active pieces.

A slightly surprising choice. I would have brought it right back to b7, leaving c6 free for the knight and d5 for the d-pawn. But that is simply a judgement call. Black has other plans.