Unschooling is a method commonly used in home education, and very popular in the UK. In the US, it is a large movement, supported by 'Growing Without Schooling' magazine.
It is a term coined by writer and educator John Holt. It is essentially synonymous with Autonomous Education, though there may be differences in degrees of autonomy.
A possible essential difference between the two terms might be that 'unschooling' refers to the practice of autonomous education in a home-based setting, with parents as facilitators, whereas autonomous education can take place in a more institutional setting as well, for example Summerhill School.
Pat Farenga, a leader in the unschooling movement in the US, defines unschooling as “allowing children as much freedom to learn in the world, as their parents can comfortably bear."
Unschooling, for lack of a better term (until people start to accept living as part and parcel of learning), is the natural way to learn.
However, this does not mean unschoolers do not take traditional classes or use curricular materials when the student, or parents and children together, decide that this is how they want to do it. Learning to read or do quadratic equations are not "natural" processes, but unschoolers nonetheless learn them when it makes sense to them to do so, not because they have reached a certain age or are compelled to do so by arbitrary authority. Therefore it isn't unusual to find unschoolers who are barely eight-years-old studying astronomy or who are ten-years-old and just learning to read.
In practice, Unschooling is the most popular method of home education in the UK (and is encouraged by Education Otherwise), and there is a very large Unschooling movement in the US.
we (I?) need to do some work on this: if we have two separate pages for unschooling and autonomous education, some of what's written on the autonomous page ought to be here instead, and we ought to add some details about how autonomous education is being used apart from by home educators.