Invisible Blocks can occur when you are mining, usually at high speed, and the client and server get out of sync on exactly which blocks have been broken.
What Are the Symptoms?
You may see what looks like an empty space, but when you try to move into it, you get pushed back. If there is an invisible block between you and a block you are trying to break, you may keep breaking that block only to have it come back time after time.
What Can be Done?
Anything that causes that space to update will fix it, such as putting a torch or another block there. But the easiest method is simply to aim at the invisible block and right click with a tool. The block will get updated and become visible and can be broken normally.