Oh, but there is gravity in space! Astronauts only FEEL like there is no gravity because they are continuously falling as if there weren't. You see, if there were no gravity in space, the astronauts in their space ships would fly off into space and not be able to come back! Imagine you have a piece of string with a ball on the end. In this example, YOU are the EARTH, the STRING is GRAVITY, and the BALL is a SPACE SHIP. Now start swinging the ball around in a circle. You see that the ball is pulling on you as you are pulling on the ball. If you were to cut the string (that is, if there were no gravity), then the ball would fly off into space. The difficult thing to realize is this: if you are constantly pulling on the string -- which you are as you swing it around -- why doesn't the ball come to you as it swings? It is because the ball is already in motion around you. This is like the space ship: it is in motion around the earth, and is continously "falling" towards the earth (as the earth's gravity pulls on it), but since it is already moving around the earth it never is pulled into the earth because it always misses.

- Answer provided by Ask Dr. Universe