Checkmate is when the king is under threat; in Check and there are no available pieces to protect the king, or if the king can’t make a legal move to a safe position. Checkmate means victory.
An example of Checkmate is shown below:


In the above example, White is Checkmated because there are no pieces that can protect the King and the King can’t capture the Queen since the Queen is backed up by a Bishop.
Another image below shows another Checkmate:

In the situation above, Black has every square around White King covered, and Black Queen has the White King in Check, resulting in an overall Checkmate since the King has no where to go and there are also no pieces to protect White King from being Captured.