Microgravity is the more accurate name for what is often called zero gravity. It is called microgravity because it describes a state where gravitational pull is present, but it is very slight. These conditions are often created artificially in space research.
Objects thrown or dropped from a height in space may appear to be floating, as if there were no gravity; but in fact the object dropped in space is falling too, it just seems to be floating because the object, the person who dropped it and the spacecraft are all falling at the same speed. If you could drop something from a great enough height, so that it was falling at the same speed as the Earth's movement, it too would be in freefall, or a microgravity environment. Even a very fast ride in a fairground can briefly give that 'zero gravity' or weightless sensation, which is similar to the condition of microgravity.