To begin at the beginning, a very good place to start...
Unschooling means many things to many people. If you take a hundred unschooling families, and asked them to define "unschooling" you would find yourself with 100 answers. This is mostly due to the very nature of unschooling, which is that it is a highly individual, life-based approach to learning.
On it's most basic level, unschooling is a form of homeschooling that is based on the belief that children learn naturally: they are able to learn what they need to know without interference, and, in fact, that they learn best when they are not hindered. It is a trust in a child's ability to learn. Unschoolers do not rely on scope-and-sequence, curriculums, lectures, worksheets, schedules, timetables, and tests.
Some "relaxed homeschoolers" unschool certain subjects. For instance, they use a curriculum to actively teach reading and math, but allow the children to freely explore all other subjects according to their interest. Many unschooling purists don't consider this to be true unschooling, but I put it out there since some families choose the unschooling label for this type of approach.
Others are full academic unschoolers, who do not actively instruct the child in any "subject." The role of the parent is seen as vastly different from that of a schoolteacher, whose primary goal is to get 20+ restless students to focus and to show a modicum of understanding of something that perhaps only a few are interested in learning in the first place. The unschooling family has a tremendous luxury in being able to allow each member to seek their own passions. The parent acts as facilitator, providing the child with opportunity, resources, encouragement, freedom, and security. The parent deeply trusts that the child can and will learn, and that the goal is to nourish a love of learning that will last a lifetime, rather than a child who can perform well on tests, but is disenchanted with learning.
Radical Unschooling is much the same, except that the trust is taken past academics/education, and is extended to all of life. RU families do not enforce routines such as bedtimes, and trust that their child can and will learn the social and moral facets of the larger society. Connection is held to be more valuable in these families than compliance, communication more than coercion.
In our family, we trust that children learn. It is what they were born to do. Children have an innate desire to be a functioning part of society and to experience meaning in their lives. Just as they learned to walk, not because of any teaching but because they were driven to do so, children learn all that they need, as they need it, in the way that they need. As a Radical Unschooling family, we find that children will learn all sorts of things without coloring workbook sheets, without coercion, without lecture. Manners. Sharing. Compassion. Cooking. Math. Spanish. Learning is something that happens every moment of every day, and we don't just encourage it, we celebrate it. We rejoice in it. We positively revel in it.