In easier to understand terms, escape
velocity is an
initial velocity one has to give to a body for it to be able to travel far enough from another body, in most cases the surface of a
planet, to escape its gravitational pull
without needing additional thrust. To be accurate, when I say
escape I mean to escape a body's gravitational pull enough to go out into space and not fall back, as we all so far know gravity's force extends throughout all of
space.
A good example would be an immensely powerful cannon that shoots a cannonball straight up into space at a muzzle velocity of 11.18 km/s from the planet we call earth. 11.18 km/s is the escape velocity of our planet.
Reaching escape velocity is not necessary to escape the gravitational pull of a planet. For example: if one can maintain a 1 mile per hour velocity constantly, one will eventually reach a distance where the gravitational pull of the earth will no longer pull it down to earth.