If a ball is thrown upwards while standing on the ground, the ball will reach a certain height (the faster thrown - the higher) and fall back down. But imagine if ball is thrown fast enough that it never falls back down, and instead travels into space farther and farther away from the Earth. The minimum speed at which this could happen is called the escape velocity.
This is, of course, a very high speed compared to how fast a ball can be thrown. Even a bullet shot into the sky will fall back down, because its initial speed of nearly 1 kilometer per second is far from escape velocity.
Spacecraft starting from the surface of Earth has a zero initial speed. But, if it has enough fuel, it may be permanently accelerated by its engine until it reaches escape velocity. Then it will travel into space even after the engine is shut off.