Montessori is based on the principles of Maria Montessori.
Here is the Wiki page about it.
But in short, your child dictates their own play/education. It seems to be quite a disciplined form of education as far as I have heard about it. Children learn early on the 'rules of society' (I think) as far as having their own play space and respecting others play spaces.
There is a focus on natural materials etc. And as far as I know, play things are played with as they are intended IYKWIM. As in, a hammer and peg set is used as a hammer and peg set, not as a boat and a rudder. (OK, terrible example!)
In some ways, it is the antithesis of Waldorf Steiner education though they have similarities, such as the focus on natural materials etc.
I think there are pros and cons to both. But I still think I like the mainstream approach as it incorporates bits of both.
Making any sense?