Unschooling is a movement in education. Basically, it can be seen as learning without school. Although unschooling may be considered a form of homeschooling, it differs from most homeschooling in that unschooling does not try to recreate the school environment at home.
Unschooling lets the child control his or her own education and learning. Instead of forcing the child to learn certain material in a certain way, unschooling consists of letting the child learn naturally on their own. Usually, this is done without a curriculum, without formal classes, and without teachers, but a child can use any of those resources if and when the child wants.
The unschooling philosophy is based in part on the belief that children are naturally curious and inquisitive. Children want to learn, and they do it best when left to explore their own curiosity.
Unschoolers often believe that schools hinder the natural learning process. In a school, the environment is too rigid and unnatural for children to learn at their best. Additionally, children are often not interested in what is being taught, since they have no choice in the matter. Having an unwanted "education" shoved down their throats turns the kids off to learning. Because children don't like school, they stop wanting to learn at all when forced to go to school.
A major problem with mainstream schools is that they can only offer a standardized, one-size-fits-all education. This does not respect the fact that children do not all learn the same. Children have different learning styles, and also have different interests and needs. In contrast to mainstream schools, unschoolers keep their children at home and allow them to explore their own individual interests in a way that they want.
While unschooling, the children like learning, and they have fun while learning. For example, a child might see a bug that interests them and the child may then want to go inside and look up information about that bug. An older child who is interested in computers might ask for a kit that would allow him or her to build a computer at home.
Since the children are following their own interests and desires, the child learns what they will want to know. For example, that child who built the computer as a kid may grow up to be a computer engineer. Had the child gone to mainstream school, the child would not have gotten the chance to explore his or her own particular interests at such an early age, and would have instead been forced to "learn" a standardized education.
Not everyone thinks unschooling is better than mainstream, standardized education. At the very least, now you know what unschooling is and some of the reasons unschoolers prefer it.