Microgravity is the environment created during weightlessness, in which gravity has a negligible effect. Microgravity is obtained in one of three ways - going far enough from any planet or star's gravity field, falling, or orbiting a celestial body — the same thing as falling but it never stops.
A common misconception is that gravity disappears when in low earth orbit (LEO), like the International Space Station. This is not the case. LEO is not far away enough from the Earth's surface to have decreased gravity - in fact, gravity there is similar to its intensity on the surface. The weightless effect is only caused because the objects on the space station and that space station are in constant free fall.
One of the most famous effects of microgravity is that a flame becomes spherical. Plants grow towards the source of the light rather than in any specific direction. This same effect can be achieved on Earth to some extent but is even more obvious in microgravity. If objects are left alone, they have a tendency to fall towards the densest part of the spacecraft. In LEO, a small amount of weight orientation is also felt as the very thin air creates a pushback effect in one direction of the orbiting spacecraft. These play a role in why the environment on a space station is called microgravity more often than zero-gravity, though both terms are used.
Microgravity was used historically on Earth's surface to produce highly spherical iron balls for buckshot. By making a tower a couple hundred feet tall and dripping molten iron from the top, the shot would form into spheres due to surface tension, then cool enough during the fall to remain undamaged when they hit the bottom. This was used to mass produce buckshot of high quality. The scientific parallel of a shot tower is the drop tower.
Microgravity is relatively harsh on human beings. It makes our muscles deteriorate, forcing constant exercise. Blood and fluids float freely around the body, sometimes causing a puffy face and stuffy nose. Extreme flatulence is common. It seems likely that once going into LEO becomes more popular, rotating space stations will be built to simulate the presence of gravity and make everybody happier.