I know people who did "unschooling," which, as far as I understand it, is basically homeschooling without much (if any?) structure. It's allowing your kids to learn about whatever catches their fancy. I've heard unschooling families say, "If they don't want to do math, don't make them do math. If they want to read all day about castles instead, let them read about castles. Eventually they'll sort it out and get everything they need, and it will come in their own time and their own way so that they're not being forced to learn things that don't interest them." The kids I've known in these situations are emotionally, socially and educationally behind others their age. (If these details are what you actually wanted in terms of elaboration, let me know. I assumed you just wanted to know what I meant by "unschooling.")
I am not certain how this practice is legal, as I homeschooled a foster child for over a year and had to follow guidelines and report to the school quarterly. I would hope all who label themselves "unschoolers" are not this extreme. I am supportive of homeschooling in many situations (although not always) but based on what I have seen and read about the "unschooling" branch of homeschooling, I am not a fan. Obviously, I'm very idealistic by nature, and dream of a perfect, happy world where we all go flitting about doing whatever we like, but the kids who are raised this way are not prepared for reality, in my opinion. I think it's great to encourage kids to pursue knowledge about topics that interest them. However, discipline and basic foundational knowledge are more useful than they are confining. Tthat's just my opinion on the subject... perhaps someone here could supply an alternative view.