A common view of space is that it is a gravity free zone. I can understand where the confusion comes from (we do call it zero gravity, after all), but there is actually a lot of gravity in space. Gravity is the reason the moon orbits the earth, the earth orbits the sun, and the sun orbits around the center of the galaxy. Gravity is a force that any object with mass will create. We're most familiar with the gravity on earth, but even a small object (like you) will have an attractive force (you can read more about that here).

For an example of what "zero gravity" really is, let's look at Commander Chris Hadfield. Commander Hadfield has been on the International Space Station since December 21st, 2012. For those of you who aren't familiar with Hadfield's internet fame he's had a twitter conversation with Captain Kirk, given Reddit the best AMA of all time, and . Now, why hasn't the ISS fallen from the sky in that time? Certainly if there were any gravity at all the entire station would come crashing down, right? The answer, which you already knew, is that the ISS is orbiting the earth. But what does it really mean to orbit?

Saying that the ISS is orbiting the earth is really just a fancy way of saying it's falling to the earth but hasn't gotten there yet. The ISS is traveling with a velocity horizontal to the earth of ~17,500 mph (Imagine a point 5 miles away from you. Traveling as fast as the ISS you'd be there in just over a second!). Commander Hadfield doesn't feel like he's moving at that speed though - he's falling to the earth at the same rate that the space station is so he feels weightless.

Here's a video of Commander Hadfield washing his hands in space: