The Zeno Paradox: Achilles walk half the distance of a tortoise at every step. If the tortoise has 1 inch of a head start, Achilles should never reach it.

It's a mental construction that should help find a solution to a problem: Why, in reality, Achilles always reach the tortoise? It's considered to be one of the earliest idea leading to the concept of quantum.

The Fermi Paradox work exactly the same.

"Where is everybody?" is a good (and funny) question. The other leg of the question being that, even at very slow sub-luminal speed, the galaxy should easily be conquered given the time period we're talking about. If you spend 100 000 years to hop from one planet to the other, then spend 100 000 year to build a new ship/crew, the galaxy should still be full by now. With Von Neumann probes it should be way faster.

If the galaxy is empty. We have a paradox. Like Achilles always reach the tortoise, there must be Aliens somewhere. It's a matter of understanding why we didn't find any.