Sometimes people say that we float in space because there is no gravity to pull us towards anything, however this isn't quite true. Let's say you were living in the international space station which is about 250 miles about the surface of the earth. The gravitational pull towards the Earth is only a little bit weaker than it is here at sea level. The reason astronauts float in the space station is that they are in free fall. It's a little bit like when you ride on a really fast roller coaster and you feel yourself lifting a little bit out of your seat. Fortunately the space station is not falling straight down towards the Earth so they never crash instead they are constantly falling away from the Earth fast enough that they never land. That's a little hard to describe in words but here's a picture that might help

Normally, things are slowed by air molecules, or dragged towards a planet by gravity. However, space behaves like a vacuum, because there are so few molecules around. You float because the attractive force of gravity in space is much less (because you're far away from massive objects like planets), and you continue to travel in the same direction because there is nothing to get in your way (like air molecules, which would normally slow you down).

Believe it or not there is a force that constantly pulls you toward the center of the earth. In fact, you are actually constantly falling toward earth at an accelerating rate of 9.8 meters per second. The force isn´t so strong that we feel like we are being pulled to the ground, but it is just strong enough to keep you on the ground. When you jump off of a wall you fall toward the ground because of downward force of gravity.

When things are in space they are also falling. The space shuttle astronauts are in is also falling. But it isn´t falling towards the earth, it is falling around the earth. The astronauts are also falling. And they are falling at the exact same rate as the space shuttle is falling. So when astronauts fall at the same speed as the space shuttle they appear to be floating. There is a very cool video that NASA made about this here:

Fantastic question! We float in space because there is very little gravitational force acting on them. Gravity is a force that is caused by the attraction of objects with mass. The planet Earth is very massive so we can feel its gravitational force when we are at or near its surface; that is why we don’t float away. The Earth’s gravity is pulling us down. When two objects get closer together, the gravitational attraction between them gets stronger; when they get farther apart, the gravitational attraction gets weaker. Because of this, you actually weigh more at sea level than you do at the top of a tall mountain. The Earth is pulling on you more when you are closer to its center of gravity.

In space, you are very far from Earth’s center of gravity (other planets have gravity as well), so it doesn’t pull very hard, and we basically float around. There is actually gravity everywhere, but it is very weak in space when you are far from Earth and other planets and stars. If you were floating out in space for a really long time, you would eventually be pulled to some massive object like the Earth or another planet.