The escape velocity is a measure of the strength of the gravity of the planet and is important for many things, but, here, we are interested in its effects on atmospheric retention. Recall some facts about orbits.

If we give an object just the right speed, it will go into orbit. If we give the object too large of a speed, it will escape the pull of the planet's gravity and run off to infinity.

The meaning of the escape velocity is then that it is the speed with which we must launch a projectile from the surface of a planet in order to have the object escape the gravitational pull of the planet.

For the Earth, the escape velocity is ~ 7 miles per second or 25,000 miles per hour!!