The original goal of chess was to capture the opponent’s king. The idea of “checkmate” follows this: you may as well call the game won/lost once capture next turn is inevitable. So you’re checkmated if whatever you do, your king would get captured next turn — i.e. if every move you can make would leave your king still in check.
In your example: There are two ways white can stop the original check, by capturing black’s queen with either the white king or rook. But each of those would leave the king in check from some other black piece — either black’s bishop, or black’s right-hand rook. So whatever white does, their king would still be in check afterwards, and so black would be able to capture it (if we still played on till the final capture).
Other answers mention terms like pinning to describe why the black rook can’t capture the white queen here. Those terms are useful for describing and understanding games, but they’re secondary to the main point here. The concept of checkmate is that it’s when whatever a player does, their king will still be in check.