The queen walks up until she is touching the enemy king, d7 against a king on d8, and because her own king on c6 is guarding her, that is the end of it.
3 Play 1.Qd7 and count what the black king has left. Nothing. The queen on d7 attacks c8 and e8 along the eighth rank, c7 and e7 along the seventh, and the king cannot capture her because the white king on c6 is one diagonal step away. He is checked, he cannot move, nothing can block, nothing can take. Mate.
Players call this the kiss of death. It is a nickname rather than a term of art, but every coach I know uses it, because the image tells a beginner exactly where the queen belongs. Not on c8, where 1.Qc8+ Kxc8 hands the game away. On d7, touching him, with her own king near enough to hold her there.
Take the protection away and it is a joke
Move the white king back to e1 and the same queen move simply loses her.
3 e That is why the whole king and queen technique is really about the king. The queen does the herding, but she can never touch the enemy king until her own king has walked over to stand two squares away, c6 against d8 in the diagram at the top. Beginners who lose this ending are almost always trying to do it with the queen alone, and I have watched a junior chase a lone king round the board for forty moves without once bringing his own king off e1.
It is one square from a stalemate
The danger sits right beside the mate. If your queen steps next to the king when your king is not defending her, you have hung her. If she covers every square around him without giving check, a queen on c7 against a king on a8 for instance, you have stalemated him and drawn a completely won game.
So before each queen move, count his squares. If the answer is zero and the move is not check, play something else. If the answer is zero and the move is check, you have just won. There is more on stalemate, and the full technique lives on the king and queen against king page.
Get the picture into your hands rather than your head: put the black king on a8, your king on e4 and your queen on h1, and finish it three times in a row without a check until the last move. Then do a set of queen endgame puzzles and watch how often the last move is exactly this one.