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It's like you get caught by the bad guy but he has run out of ammunition so you get to escape with a draw where otherwise he would have won.

@OP: When neither player has enough material with which to checkmate, the game ends immediately, as a draw by insufficient material. The scenarios that cause this are:

1) King vs. King

2) King vs. King and Bishop

3) King vs. King and Knight

4) King and Bishop vs. King and Bishop, if both Bishops travel on the same color squares.

Never offer a draw in King vs King + bishop!  There's a chance your opponent could mess up and you'd win.  Remember, no one ever won a game by drawing!

thanks, every reply was helpful.

@OP: Except for waffllemaster's post, which is apparently an attempt at jocularity. Just to clarify: the scenario King vs. King and Bishop is an automatic draw, so you will not be given an opportunity to offer a draw.

Ever play Pictionary? 

It does not have to be both sides with insufficient material.

If your opponent has a king and a pawn and you have a king you cannot deliver checkmate (material insufficient) but your opponent could queen his or her pawn so their material is not insufficient.

But if they take so long trying to queen the pawn and deliver mate that they run out of time they would normally then lose the game on time.  But, because of the insufficient material rule they do not lose, instead the game is a draw.

This rule seems to cause much annoyance as there is an indignant thread started about it here on many days.

This is true. When one side runs out of time, more scenarios are included in the insufficient material rule. The four I explained above do not necessarily take running out of time into consideration.