This either means that you don't understand something or that you don't agree with it. For example, if you're waiting for a long time on an airplane for it to take off, you can say to the person who's riding with you:
I don't see what's taking so long.
This means that you don't understand why it's taking such a long time, and you're angry about it. So "I don't see ___" is used when you don't understand the reason for something and you don't think that there really is a good reason.
Here are some more examples with different endings:
I don't see why not.
I don't see how that's possible.