Permaculture is not a word. It's a paragraph. Some of what I'm putting here is controversial. Permaculture at it's core, it's a way of thinking about the world and solving problems in a systematic way that goes beyond sustainable. As Geoff Lawton says, "Don't plant a tree; plant an ecosystem." It's high level practitioners are able to achieve feats that are seemingly miraculous (see video for an example).
The word was coined by Bill Mollison and David Holmgren. Bill Mollison put together a course describing the system, and anyone who has taken a PDC (Permaculture Design Course) does permaculture and can use officially use the word. Of course anyone can learn or use Permaculture.
Unfortunately, there is quite a bit of infighting in permaculture (mostly among posers). As an example, Mollison and Holmgren told Sepp Holzer that they thought that what he practiced was permaculture and wanted him to use the word, but other lesser practitioners insist that Holzer does not practice permaculture as he has not taken a PDC.
Another problem with permaculture is that it is infested with hippies. There's nothing wrong with hippies per se, but a large proportion of them seem to do a lot of hating in the name of love. Another problem with some hippies is what I call toddler syndrome, "What mine is mine, and what's your is mine." Some of them will accuse successful permaculturists of not following the permaculture ethics because they make a profit and do not share it with the accuser.
Note that the high level practitioners such as Geoff Lawton do not share this view. Moreover, these two issues have subsided somewhat as the two of most prominent permaculture practitioners in the U.S. are pro-profit and pro-results. Their influence has helped attract a large number of new people to the movement who do not share the hippie hang ups.
Personally, I see permaculture as a way that Christians can fulfill the first commandment in the Bible, to fill the earth and have dominion over it. Destroying the earth somehow doesn't seem to be an appropriate part of that plan. Whatever you believe about carbon, there is no doubt that humans have destroyed a large number of resources, most spectacularly seen in the desertification of the Fertile Crescent and sub-Saharan Africa. I think that more Christians should be involved in Permaculture as a way to help the poor, improve their own lifestyles, and fulfill God's commands.
With that introduction, here are some permaculture resources:
My favorite way to learn about things. My two favorite for permaculture are Jack Spirko's and Paul Wheaton's. However, as they cover a lot of topics, not just permaculture, I have excerpted highlighted episodes below. (Warning: Paul has a tendency to ramble and get off topic and cusses occasionally).
Jack Spirko TSP Podcasts
Paul Wheaton's Podcasts
Permaculture Rockstars (in Progress)