I don't understand what escape velocity is. I know escape velocity from the earth is 11,186m/s. If a rocket is launched from the surface of the earth with initial speed of 11,186m/s, does it escape the influence of earth's gravitational pull? Or does it need to have that velocity at a particular distance from the surface to escape the gravitational pull?
to hoist a rocket up off the surface of the earth and send it coasting away into outer space requires the expenditure of a definite amount of energy. you can impart that amount of energy to the rocket by boosting it off the ground with a certain speed, which is what is called the escape velocity. that velocity is exactly enough to keep the rocket moving ever farther away from the earth, even though the earth's gravity never stops trying to pull it back.
And even though the rocket is being progressively slowed down by the pull of gravity, that pull gets weaker and weaker the farther away from the earth the rocket gets. In the end, the rocket loses its velocity at the same rate by which gravity fades away and it then drifts off, slower and slower and slower, becoming ever closer to being free of the earth's gravity.
If the rocket is launched slower than escape velocity, gravity will eventually win the battle and bring the rocket crashing back down to earth. If the rocket is launched faster than escape velocity, its velocity wins the battle and it sails off into space without stopping, never to return.
Simply put, any object sent from the earth's surface or anything that is moving away from the earth's surface with the escape velocity (or greater than that) will permanently escape from the earth's gravitational pull and move to infinity. The earth's gravity won't be working on that object any more from then on.