Homeschooling is a way of educating children at home. In USA, it is allowed and it should be in other countries. The original idea of homeschooling was to educate children who would do better home than in American public schools. The psychological effect of school makes children less interested in learning things, after all they're forced to study rather than exploring things on their own. The parents who educate their children this way are most likely to be very educated themselves. Unfortunately, it is often used by conservatives as a means of feeding religious propaganda to their children.
Sometimes home schooling can be good, for example if a child has been bullied at school for being gay, for being different or even because of his/her race --then home schooling is one way to help them learn better by removing them from a stressful environment. While traditionally the home schooling system was a pen-and-paper system just like public school, now online schooling is becoming popular as well, with some of its most notable advantages being a ready-made, standardized curriculum that takes pressure off the family, and building rapport with experienced teachers. Most states now have programs that offer fully accredited, tuition-free online schooling all the way from kindergarten through high school.
Good home schooling parents make sure their children mix with other children at clubs, and other fun places. There are various organizations that focus on home-schooled children and on getting them together to provide some social interaction.
Sadly the parents who are mad Christian fundies abuse this law in order to limit their child's knowledge and to make them believe things like Intelligent Design and Young Earth Creationism. That is not education, due to the fact they teach their children things which conflict with science and logic. To these parents it is more important for their child to be a devoted Christian rather than being educated and equipped for finding a job.
Fortunately, only 2% of America's parents buy into this excuse to turn their kids into religious ignoramuses, but that's still too many. When religiously home-schooled youngsters grow up they can have trouble fitting into normal society because they haven't learned to mix with normal people at school. Unlike the example of good homeschooling above, many of the bad examples of homeschooling include isolation from adults and kids outside the parents religious fundamentalist community and even isolation from other kids their age, so that no outside "bad influences" can "harm" the child.
That can make it difficult for them to find and keep good jobs or do well at university. Religiously home schooled kids learn how to mix with their own crazy religious community because they went there every Sunday and sometimes during weekdays too throughout their childhood.