This is a question of force. I suppose that everything in physics is a matter of force though. But for your question, it's most definitely forces. Another thing to keep in mind is that all forces come in pairs. That's outlined in Newton's third law of motion. That's the equal and opposite force law.
Let's start with standing. When you are standing, you are not moving downward and not moving upward. There is no change in motion, so all of the forces acting on you are balanced. I'll work with two forces to simplify. Gravity is pulling down with a force of "x." Your legs are pushing up with exactly the force of "x" as well. These two forces combine for a net force of zero. Think of it like adding a negative 10 to a positive 10. The net is zero.
When you jump, your legs are providing a downward force on the ground. Newton's third then says that the ground is providing the same sized force on your legs in the opposite direction -- up. As long as that upward force is greater than the downward force of gravity, you will accelerate upward into the air. You have created an unbalanced set of forces. Gravity will eventually become a larger acceleration force than your upward jumping movement. At that point, you will begin falling downward and land. Jump complete.