Permaculture was conceived, back in the 1970s, as a design system which uses natural ecosystems as the model. Consider a wheat field that's bordered by some unmanaged woodland. 
The wood contains a range of plants from herbs, shrubs and climbing plants to trees of differing sizes; fungi; birds, animals and insects. The wheat field is monocultural. The woodland has far more biodiversity and a far greater biomass than the equivalent area of wheat field and you don't have to do a thing to achieve all that, it just gets on with it. In contrast the wheat field must be manured, ploughed, harrowed, and probably sprayed several times a year with herbicides, pesticides and fungicides. The big 'BUT' is that we can eat much more of the wheat field than we can of the woodland. Permaculture is about designing an edible landscape, modelled around an ecosystem like the woodland, choosing plants etc., to make a larger proportion fit for the kitchen. An example of this is the forest garden. (see diagram below © Graham Burnett)
It's important to say that permaculture means many things to many people, it's constantly evolving and developing and is much more widely applicable now. Patrick Whitefield (who I did my Permaculture Design Course with) makes a distinction between the example at the top, which he calls 'Original Permaculture' and what he calls 'Design Permaculture.' We go back to the woodland example but then consider how it functions so well and we see a great diversity of beneficial relationships between all the plants and animals, insects, microbes, etc., that make it up.
Thinking before we act, we consider what we want to achieve, what we need to do to achieve that, then think about beneficial relationships between different components of our systems: outputs of the chicken house, such as the manure, become inputs of the vegetable patch, trimming from our willow arbour become goat and rabbit food. We think about where we're going to put everything, relative to our house and the other components. For example, herbs should be right next to the kitchen door and an apple tree, that only needs a few visits a year, can be at the end of the garden. But consider also that a fruit tree might benefit from being grown up the south wall of the house and thus ripen better with all that stored warmth, so it's not black and white; permaculture is not a set of rules.
We can go a stage further and think about our lives or projects as a whole system that can benefit from applying permaculture principles: working out the most effective way to do things, that involves the least effort and the least damage to others, and looking for ways to make relationships between elements of our lives more beneficial. This could include choosing what we eat, how we travel, the type of work we do, and where we live, to working with others to create, for example, a community food-growing project. It's about making decisions that relate to all our other decisions; so one area of our life is not working against another. For example, if we are planning a car journey, consider other tasks that can be completed on the way to our destination (combining a trip to the leisure centre with buying food on the way home, for example).
This is just my own attempt at trying to explain what Permaculture might be (borrowing from Patrick Whitefield's temperate climate permaculture handbook, The Earth Care Manual and from the permaculture.org.uk website. Then there are Permaculture's ethics and principles: Earthcare, People care and Fairshares. In fact, there is lots more to learn and understand and you could start by typing in 'permaculture' to your search engine of choice.
Permaculture in Brittany.
We're still consider ourselves beginners in permaculture, so are learning ourselves and whilst we have many things already established we're constantly working on introducing new elements. We've redesigned the gite garden to turn it into a working example of permaculture in a small space. It's a low-maintenance garden and includes a delightful chamomile lawn which needs no mowing, stays green in the summer and gives off a wonderful scent the year round. There are also fruit and nut trees, vegetables and herbs and we encourage guest to pick and eat whatever they find in season.
We are going to build a straw-bale house with as small an ecological footprint as possible. And we'll be installing a plant filter and pond sewage system. You can see what we're up to by having a nose at our permaculture blog .
♦♦ I'm going to do some more work to this page, to include a drop-down menu detailing the elements of our own permaculture smallholding, with free factsheets and useful links; watch this space.
In the meantime, you can read some magazine articles I've written by clicking on the links; the articles will open as PDF files.
Read the article we wrote for Permaculture Magazine on making organic woollen duvets
and the follow-up article we wrote about a Somerset sheep farmer and the wool trade.