Microgravity is where gravity is (almost) the only force, or where you cannot feel gravity.
In a spaceship, for example, people don't feel they are being attracted towards Earth. Of course, any experimental system, e.g. a fluid experimental setup wouldn't feel that force, if they could feel. However, this does not mean that there is no gravity at all. Many people mistakenly think that gravity does not exist in space. After all, we face a situation in which the Space Station -and what is inside it- are attracted by Earth and nothing else interferes with them. We can express the definition of microgravity in other words:
Microgravity is where weights do measure only millionths of your weight on Earth.
This is the origin of the prefix "micro" in microgravity. As a consequence of this, if one astronaut measures his weight in the Space Station, the astronaut and the weight he is on would be flying in the same direction, so the astronaut wouldn't exert (almost) any force on the weight, measuring only millionths of his weight on Earth.
Microgravity, also called zero-gravity or weightlessness, is the absence of gravity. So that, a micro-g environment is one where the acceleration induced by gravity has little or no measurable effect, gravity itself does not change. It is best illustrated by astronauts floating in their spacecraft or in an parabolic flight.
Source: ESA EAC
One of the most promising areas for the commercialization of space is in the field of microgravity. Microgravity allows the research and development of new materials which cannot be made on Earth due to gravity. These new materials can be used to speed up future computers, reduce pollution, improve fiber optics, and enable medical breakthroughs to cure diseases.