Maniakes over at Dean’s World has a good post explaining what a Public Good is.
A public good is a good which is nonexcludable (you can’t keep people from partaking in the benefits of its existance) and nonrival (my partaking in the good does not inferfere with yours). National defense is the classic example of a public good — it’s nonexcludable because you can’t turn off the national defense to my house if I don’t pay my Army bill, and it’s nonrival because keeping Russian paratroopers away from my house doesn’t interfere with keeping Russian paratroopers away from my neighbor’s house. Pizza is a classic example of a pure private good — it’s excludable (if you don’t pay for the pizza, you don’t get a slice) and it’s rival (each slice you eat is one fewer I can eat).
Public goods are interesting to economists because the market doesn’t handle them very well because of the nonexcludablity aspect — I start up a National Defense Company, I’ll have a lot of problems getting people to pay their army bills because what am I going to do if they don’t pay — and the nonrival aspect works around a common problem with the government providing goods for free — free government pizza wouldn’t work because people would eat too much and we’d run out or have to spend a lot of money making more, but free national defense works fine because your consumption doesn’t interfere with mine. So even very free-market economists often favor government provision of public goods.
Government provision is not the only way to handle the public goods problem. Another way is to change what you’re selling to something that is excludable. Broadcast radio is a good example of a public good that the market has found a way to provide. You can’t sell the broadcast itself, because that goes everywhere. But you can sell advertising mixed in with the content, because you can refuse to run ads from people who don’t pay. And you can also encrypt the broadcast signal (as XM and Sirus do) and sell decryption devices.
Education is often described as a public good. It isn’t. You can throw out students who don’t pay their school bills (excludable), and there’s only so many people who can fit in the classroom (rival). Education does have positive externalities, but most of the benefit fo education fall on the students themselves.