One of the biggest benefits of private schools is their attention to each individual child. Through small class sizes, the attention of dedicated teachers, and specific educational philosophies that target the learning habits of your child, private schools offer an environment that challenges a student's academics, while keeping a close eye to make sure they are succeeding.
Private schools are also open to more parental involvement and staff are quicker to respond to parental concerns. So if a parent is ever worried about the progress of a child, they are encouraged to get their teacher involved. Vice versa, a teacher will often contact the parent if a child's academics begin to waver.
If a student has special needs and is falling behind in public school, a special needs school can be a valuable option in helping them catch up to their peers, or in getting their graduate diploma. This article has a great summary about all the different types of special needs schools that exist, and you can find a ,a href="http://www.ourkids.net/special-needs-schools.php#schoollist"list of special needs schools here.