The International Space Station is in low earth orbit, approximately 360km above the surface of the Earth. They experience microgravity. I always assumed this is because they are far enough from the earth that the Earth's gravity no longer had a significant impact at this altitude.
It turns out I'm wrong. Gravity only reduces by about 3% for each 100km altitude. So they're still experiencing 91% of the gravity that we
What we experience as weight is known as "Apparent Weight". It is perceived because of force gradients across our body, where each horizontal cross-section of our body is supporting the weight of the parts of our body above the cross section.
When we're standing on the ground, we experience weight due to the reaction force of the ground. When in an aircraft, gravity acts on all mass within the aircraft (including our bodies), but the lift is generated by the aircraft shell, which also causes a reaction force that triggers apparent weight. The fact that gravity acts on all objects in the aircraft, but lift is only generated by the aircraft shell creates this force differential. If you were in a box that was in free-fall (ignoring friction for the moment), you would experience weightlessness because there is no reaction force provided by the box.
So back to the astronauts... They still experience gravity, but it is balanced by the centripedal force created by their orbit around earth. They experience weightlessness because the space station is moving at the same rate and with no friction does not provide a reaction force.
This has got to be my most confusing post yet! As always, for more information, see this Wikipedia article
