Now that the one word answer's out of the way, I of course owe you an explanation. You probably love looking out of car windows (I know I do!), especially if it's going fast. Have you ever noticed how other cars going the same way (maybe in the next lane) don't seem to be moving as fast as the countryside (or houses, or shrubs, etc.)? And if you happened to look at the head-on traffic in some other lane, they would seem to be moving faster than the houses! By now, you've probably figured out the rule of thumb; if you're going in the same direction as someone else at nearly the same speed, you don't see him zooming by; he seems to be going much slower than he actually is. But if someone is approaching you, you think he's going faster than either of you really are ("actually is", "really are", all refer to the speed on your speedometer, i.e., with respect to the ground beneath you).

All this can be neatly summed up in a little arithmetic, called addition of velocities. All this says is that if you're moving at a certain speed and watching someone else moving at some other speed, then the other person will appear to move only as fast as the difference of your speeds. This is why cars going the same way seem to be moving quite slowly, while head-on traffic seems to zoom by! What's more, it turns out that the same law applies for acceleration too, which tells you how quickly you change speeds. In other words, if you and your friend have the same car, and both of you hit the gas pedal equally hard, while both of you rapidly gain speed, your friend will seem to be hardly accelerating away from you!

So far so good; but you're probably asking yourself, "What does this have to do with gravity?" Gravity can be completely described by the acceleration it produces. For example, the acceleration of a baseball in the air (as well as falling raindrops, or anything else, for that matter) is roughly 10 m/s² near the Earth's surface. This simply means that Earth's gravity pulls everything down with the same acceleration. The weight we feel is simply because the ground beneath us is resisting the gravity. It is keeping us from falling through at 10 m/s². In other words, the weight we feel is due to our relative acceleration with respect to whatever we are standing on (of course, the ground is static, and hence our relative acceleration is still 10 m/s².) Now suppose you were standing on something that was also accelerating downward, but at 2 m/s². Then you'd feel lighter, since your relative acceleration would only be 8 m/s². This is exactly what you feel when an elevator starts going down from rest. Better still, this is the cause of the queer sensation you get when you're in a roller coaster that's plunging down. How about if whatever you were standing on was also falling at 10 m/s²? Then you'd feel "weightless" since your relative acceleration would be zero! For example, if the elevator chord breaks (God forbid!), then the Earth would pull you and the elevator down at 10 m/s², hence your relative acceleration with respect to the elevator floor would be zero, and you'd feel as if there's "zero gravity"!

This is exactly what happens in space. Astronauts up in space are feeling not only Earth's gravity, but also the sun's, the moon's, maybe Mars', and so on. However, so is the spaceship! Hence, both of them are "falling" (wherever they might fall) with the same acceleration. Since the astronaut has only the spaceship to stand/sit/lie in, he feels no relative acceleration with respect to it, and hence "weightless". This is what is popularly (mis)represented as "zero gravity" (probably sounds funkier than "weightless"; I don't know!).