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Aristotle believed that to keep something in motion, there must be a constant force acting on it.This is also known as Aristotle's Fallacy in many textbooks of Physics.
For example, to make a train go, you have to constantly run it's engine to cause the motion.
Galileo rectified this idea by introducing the idea of inertia. He suggested that everything in motion must continue to be in motion due to an inherent property called inertia. The inertia of rest on the other hand keeps things at rest at rest.
The agency that can bring about a change in an object's velocity, is what he termed as force.
To summarize, Galileo called force the agency that gave a body an acceleration whereas Aristotle believed that force is required to maintain velocity.