Escape Speed is weird

[envscigrl]

problem:
Taking the potential energy to be zero at infinite separation, find the potential energy of a 118.0-kg object at the surface of the earth. (Use 6.37E+6 m for the earth's radius.)
I did this and got -7.374E09.
It then asks Find the escape speed for a body projected from this height.
I do not understand the concept of escape speed. In my book it gives this equation: sqrt 2gRe
It then goes on to solve the equation to be 11.2km/s.
How do I use this equation or the concept of escape speed to solve this problem.
Thanks for the help.

[CartoonKid]

It's just the simplification of (1/2)mv^2=[G(Me)m]/(Re). For the object to escape to infinity, its kinetic energy must at least equal to its potential energy on the earth because that much of work has to be done to bring the object to the infinity.

[envscigrl]

Thank you very much that makes a lot of sense!