Like the name implies, these phones are designed to function until the minutes package you purchase has been depleted. After that, you pitch the phone. There are a variety of disposable cell phones on the market, but they typically have limited functionality and carry a bargain basement price tag.
Disposable phones may not be efficient (or green) as a long-term solution, but for a small introductory test period, they'll give your child some practical experience using a cell phone without much risk to you. If he loses the disposable, you won't be out much money, and your child will have learned a valuable lesson. A bad experience might even give you a breather before having to revisit the cell phone discussion again in a month or two.
If your child does treat the phone responsibly, you'll probably feel more comfortable buying him a quality phone and adding him to your family calling plan (with the increased risk of higher-than-expected usage). If there's some initial grousing regarding the disposable option, you can explain that a successful test period may encourage you to opt for a better permanent phone than you would otherwise. Everybody wins.
Disposable phones are also good fall-back options if your child is hard on his stuff and he's going away to camp or to visit relatives for a few weeks. If the phone ends up at the bottom of a lake somewhere, no harm done.