The word "permaculture" comes from "permanent agriculture"; it is an approach to producing food by working in harmony with the land, in order to minimize the labor involved in doing it. Permaculture is involved with both growing crops and raising animals for food. Some people have called it "the lazy person's farming" because its objectives are to grow/raise the food you need with minimal work.
How is that possible? Well, first of all, notice we didn't say "no work" - but the principles of permaculture allow us to be as self-sufficient as possible (given the resources we have - land, etc.) without having to devote full time to just food production. Here are some web sites to help you understand what Permaculture is all about:
Introduction to Permaculture: Concepts and Resources
This is a sub-site within the National Sustainable Agriculture
Information Service's site.
It is a free introduction to permaculture, and includes a
thorough list of references on the topic.
This is a very good place to start learning about permaculture.
The Permaculture Institute
Located near Santa Fe, New Mexico, the Permaculture Institute
was founded in 1997 to promote sustainable living skills
through education, networking and demonstration projects.
Though they are headquartered in the southwest, they have
programs throughout the United States.
Permaculture Research Institute of Australia
This site relates more to Australia than to the United States
(though the principles are good worldwide).
I've included it on this list because the institute was
founded by Bill Mollison, one of the creators of permaculture.
Permaculture Activist
This is the web site for "Permaculture Activist," a quarterly
magazine with news and resources for permaculturists around
the world.
It has been in business for over 20 years, reporting on
permaculture projects, both underway and completed.