This means "I don't think it's going to happen." You use this when someone suggests that something will happen, but you don't believe it.

This is a slightly casual phrase. A more formal way of expressing this idea is:

I don't think that's likely to happen.

"I don't see ___" can be completed with specific actions as well, instead of "that happening". For example:

I don't see Joe agreeing to do that.

This sentence means "I don't think that Joe will agree to do that."