Escape velocity is defined to be the minimum velocity an object must have in order to escape the gravitational field of the earth, that is, escape the earth without ever falling back.

The object must have greater energy than its gravitational binding energy to escape the earth's gravitational field. So:

1/2 mv2 = GMm/R

Where m is the mass of the object, M mass of the earth, G is the gravitational constant, R is the radius of the earth, and v is the escape velocity. It simplifies to:

v = sqrt(2GM/R)

or

v = sqrt(2gR)

Where g is acceleration of gravity on the earth's surface.

The value evaluates to be approximately:

11100 m/s
40200 km/h
25000 mi/h


So, an object which has this velocity at the surface of the earth, will totally escape the earth's gravitational field (ignoring the losses due to the atmosphere.)
It is all there is to it.