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
When a player has no legal moves available and his/her King is not in check the game is a draw (stalemate).
Some think that this is illogical or even unjust.
They do have a point, but let me observe that if stalemate were considered a loss for the moveless player, all K+P/K endgames would be won by the stronger side. This may result in overcautious play in the opening and middlegame as a material advantage of one pawn would be much more sensible than it is now.
Sacrificing a pawn for the initiative would be a way riskier business.
Overall, declaring stalemate a win could result in a slower and less dynamic (less fun?) game.
The answer given by Captain_Shepard is correct. In Chess, stalemate is a draw. However, the OP's confusion might well be justified as Chess is unusual in this regard. Many games have stalemate as a loss for the player who cannot move. For example, Chinese Chess or Xiangqi (which is based on the same precursor game as Chess and is therefore very similar) has stalemate as a loss.
Thanks to jnkappen's answer, I did a Google search and found this interesting Wikipedia article: http://en.wikipedia.org/wiki/Stalemate#History_of_the_stalemate_rule
Like GM Larry Kaufman mentioned in that article, I am of the opinion that stalemate being a draw is illogical and should be a win for the player administering stalemate.
According to The Laws of Chess:
5.2.a The game is drawn when the player to move has no legal move and his king is not in check. The game is said to end in ‘stalemate’. This immediately ends the game [...]
This is the situation you described.