Gravity is an attractive force between objects. Any piece of matter has a certain amount of mass ("stuff" that takes up space), which will attract other objects with mass; this is what is called gravity. Objects with more mass will experience a stronger attraction to each other. The farther away these objects are from each other, the less they will be attracted to each other.
Albert Einstein suggested a slightly different definition of gravity. He said that objects with mass will "bend" the shape of the universe to make it look like there is an attractive force. Lets imagine that the universe is like one big, flat piece of foam padding. If we put a heavy steel ball on the foam it will create a depression in the foam around itself. Now, if we roll marbles over the foam padding the marbles that are close to the steel ball will fall into the depression that the ball has created. The steel ball attracted the marbles by bending the foam padding just like masses in the universe attract each other by bending the shape of the universe.