Maria Montessori was an Italian physician and educator. As she began working with children she came to the conclusion of a few things children need, which are:
1.) responsibility (which is basically the kids learning self-discipline, caring for people around them, and engaging in social context),
2.) self-discipline, and
3.) concentration (where kids have lengthy periods of study and exploration)
Within Montessori, there is an emphasis on independence. Children are given access to materials to master in a logical and sequential order. It’s a mode of self-discovery, and although there are limits, there is freedom within the boundaries. Not all children work well within the Montessori method of learning. It is extremely different than a traditional classroom because of its constructivist nature (as opposed to a teacher telling them what to learn).
I hope this video helps you understand a bit about the background of Montessori. Here are a few links you can check out to get further info on Montessori and integrating it into your homeschool:
http://mymontessorimoments.com/2011/03/07/as-promised/ (her classroom setup in her home)