If you unblock something, you free it or clear it of anything that's in its way. A plumber's frequent task is to unblock pipes so water can move through them.
You can unblock your stuffed-up nose by blowing into a tissue, or unblock the driveway by moving your bike into the garage. Cardiologists, or heart doctors, often need to operate on patients in order to unblock their clogged arteries, so blood can flow freely. Unblock comes from adding the "reversal" prefix un- to the verb block, "obstruct or hinder passage."