user9148: Checkmate means king is in trap and there is no way out.
If it is my turn and opponent's king has a way out from trap, am I said to win the game? 
EDIT: Suppose my rook is in the adjacent column w.r.t opponent's king and I move my rook so that it is in the same column with free space by the position of King. Opponent somehow doesn't observe the check and make a move that can't break my check. Now, it's my turn and Let king has all 6 ways out from the check. But after alll it's my turn so is King checkmated or not?

user-1: Checkmate means shāh māt in Persian, i.e. the King is helpless.
This means 2 conditions must be met:

The enemy king is in check
There are no legal moves to get the king out of check, e.g. there are no moves to capture the checking piece(s), or to move the king away or to block the check

N.B. When considering whether the king can get out of check, note that castling is not a legal move, as a king cannot castle into, out of, or through check.
The situation you describe seems to have been a mistake, made through a combination of illegal moves. In this case, there are 2 options:

Restore the last legal position, which is what I would recommend for friendly games
In a tournament setting, illegal moves may result in a loss for the player making the illegal moves. Check with the arbiter in this case


9148: <p>Checkmate means king is in trap and there is no way out.</p>

<p>If it is my turn and opponent's king has a way out from trap, am I said to win the game? </p>

<p>EDIT: Suppose my rook is in the adjacent column w.r.t opponent's king and I move my rook so that it is in the same column with free space by the position of King. Opponent somehow doesn't observe the check and make a move that can't break my check. Now, it's my turn and Let king has all 6 ways out from the check. But after alll it's my turn so is King checkmated or not?</p>
 -1: <p>Checkmate means <em>shāh māt</em> in Persian, i.e. <em>the King is helpless</em>.</p>

<p>This means 2 conditions must be met:</p>

<ul>
<li>The enemy king is in check</li>
<li>There are no legal moves to get the king out of check, e.g. there are no moves to capture the checking piece(s), or to move the king away or to block the check</li>
</ul>

<p>N.B. When considering whether the king can get out of check, note that castling is not a legal move, as a king cannot castle into, out of, or through check.</p>

<p>The situation you describe seems to have been a mistake, made through a combination of illegal moves. In this case, there are 2 options:</p>

<ul>
<li>Restore the last legal position, which is what I would recommend for friendly games</li>
<li>In a tournament setting, illegal moves may result in a loss for the player making the illegal moves. Check with the arbiter in this case</li>
</ul>
