Only the king remains, but he is stuck, can't move I played with my friend yesterday, and we reached a point when I cornered him from everywhere. I had a queen and a king, and he had only his king left, but he could not do any move because any move would be considered checkmate. So he told me it's a draw because it's a stalling position. Is that true?
If you mean he can't move his king anywhere because if he does his king will be in check, but none of your pieces are attacking him at the moment, and it's his turn, then yes, it's called a stalemate because he has nothing to play but his king isn't attacked by any one of your pieces, and this is a draw. 

P.S. that is if none of his pieces are able to move, if he has another piece which he can play with it's not a stalemate. xD