Gravity is a force by which all physical bodies attract each other. Gravity is what is holding you to the ground, and what holds the moon in it's orbit near earth. Due to it's mass, our planet has an enormous amount of gravity force, but even your body has a small force of gravity.
Earth's gravity force is about 32.2 feet/second squared. If you throw a ball up in the air, it is constantly accelerating back toward earth at 32.2 feet/second squared. Even on the way up, it's speed is slowing at that rate, then for a brief moment it's not heading up or down, and then the ball accelerates at 32.2 feet/second squared downward until it hits the ground.
Newton's law of universal gravitation is this:

Where F is the force, m1 and m2 are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant (or 32.2 feet per second squared).
Using this equation, you could figure out how much force F your body exerts on, say, a 16 pound bowling ball.