Force is related to acceleration because F= mass X acceleration.
Velocity is speed with a direction included. For example, 35 mph is a speed, but 35mph north is a velocity.
Acceleration is the rate at which velocity changes. Say that over the course of 10 seconds, a car goes from zero to 100 meters per second. The car increases its velocity 10 meters per second every second. So the acceleration is 10 meters per second squared.
For you Calculus types:
Acceleration is the derivitive of velocity with respect to x.
Velocity is the integeral of Acceleration with respect to x.