between a rock and a hard place.

[keannu]

This means you can't do either this or that as if you were stranded somewhere. What does "hard place" mean? Do you know its origin? The book says it's from Odyssey in Trojan war who encounted a rock island of a monster and tried to avoid it but to meet with whirlpool.

A: Jimmy, are you going to Mary's birthday party?
B : Well, I promised Mary I would go. But my music teacher also performs in a concert that same night.
A: It sounds like you're stuck between a rock and a hard place.
B : I don't know what to do!

[SoothingDave]

Between a rock and a hard place: Information from Answers.com

It means that you have two choices and either choice will cause you difficulties. in the example you give, one can either satisfy Mary or the teacher, but not both.