The plantar fascia is a thick tissue on the bottom of the foot that connects the heel and the ball of the foot. Here's a good overview of the condition from the NIH.
When it's really, really bad, some people even have surgery, but there are a lot of things that can help you avoid surgery (and feel a whole lot better!).
1 - Shoes
Make sure you have a good pair of shoes, with good arch supports. Scrimp somewhere else, not on your shoes! Going barefoot is hard on PF, so wear them as much as possible. Crocs (Caymens/Classics) are pretty good, and are close to going barefoot for summer wear. Some styles of New Balance (I've had good luck with 927), and Birkenstocks are some others to look at. On footsmart.com you can search for shoes by condition (even if you don't buy there) to see what might be a good choice, or try a google search.
2 - Stretching
Do it, multiple times per day, but START GENTLY. (If you cause more tears by over stretching, you aren't helping your injury). I've come to accept I can never stop stretching (because I stopped after I got better 2 years ago, and ended up right back where I started after a winter with less walking!) This page has a short video demonstrating a couple of basic exercises. A google search will turn up lots of results.
4 great stretches are the towel stretch, the calf stretch, the stair-step stretch, and the frozen can roll/foot massage. This last one is really nice in the summer when you are sitting at the computer. Put a plastic water bottle in the freezer, and then roll your foot back and forth over it as much as you can stand, up to 20 minutes, while you surf! Much more economical than purchasing a roller!
If you have any stairs in your home, the stair-step stretch is easy to incorporate. Just stop for 30 seconds on your way up the stairs. Hold the railing for balance and let your heels hang off the edge of the step, and gently apply your weight until you feel a good stretch.
Once you get back to being able to exercise & aren't struggling with it, you may be able to go barefoot sometimes (though crocs are close to barefoot), but don't stop stretching.
3 - Activities
Limit the activities that led to your PF and stay off of your feet as much as possible for a week or two while you do the stretches. Then, after at least 2 weeks, or maybe a month, you can try adding back in some gentle exercise, but really keep it toned down. For example, if you usually walk 3 miles, do a short walk, only half a mile or mile at the most. Make sure you stretch before hand, or you'll regret it the next day! Gradually you'll be able to build back up and have pain-free exercise.
4 - Products and Accessories
A night splint like this one from footsmart.com can help. I have also worn it on occasion during the day. You can't walk with it on, but if you have 30-60 minutes to put your leg up and watch TV or read, that's a good time to also use the splint. At night I tend to wear it about half the night and then kick it off. Some people like the Strassburg sock, but I found that instead of stretching the fascia it mostly put a lot of pressure on my toes and was very painful no matter how much I tried to loosen it. I couldn't wear it for even 30 seconds. The manufacturer did take my return though.