Why is this a checkmate? I'm new to chess and I'm confused about a puzzle I was practicing.

As you can see my black queen has put the white king in check, but I'm confused how this is possible if a rook is right next to my queen and could capture me next turn. Am I missing something?
To get out of check, the king needs to move to a square that isn't attacked by any opposing pieces, or you need to capture/block attacking pieces such that the king is no longer under attack on its current square.
Since the queen is attacking the king and both of the unblocked squares it can move to, white needs to capture the queen to get out of check here. The only two pieces in position to attempt this are the king and the rook. The king cannot do because it would be attacked by the black rook if it did, and the rook cannot do it since it would expose the king to being attacked by black's dark-squared bishop.
This situation is called pinning: the bishop has &quot;pinned&quot; the rook (even if the queen weren't there) because moving the rook would expose the king to capture, and it is illegal to make a move which places your own king in check. This term is also used when the piece you expose by moving is a high-value piece other than the king (typically a queen or rook), but in this case it's not illegal to make the move, it's just a bad idea most of the time.