Throughout time, chickens have been bred for two specific purposes. The first and most obvious purpose is the healthy, nutrient-rich eggs they lay. The second is their meat, which is an excellent source of lean protien. Nowadays, many people utilize chickens' egg laying capabilities, but many people wonder if it is okay to eat the chickens you raise in your own backyard. People usually consider this when they are deciding what to do with a hen that has stopped laying eggs or an obnoxious rooster.
The simple answer is yes, you can eat your chickens. However, chickens too old to lay eggs usualy produce tough, chewy meat. Younger chickens in their prime are are much better to eat, but the meat will still be tougher that what you buy at the grocery store. (This makes sense. The meat you buy at the store is usually from birds confined to cages all day, who rarely use their muscles. Also, these chickens are specifically and intentionally fattened.) One solution many people try is slow-cooking the bird. This will help, but not typically solve, the problem.
When eating a backyard chicken, it is especially important to clean and cook the meat well, as salmonella can be a concern if the meat is not properly prepared.
Also, please be sure to kill the chickens humanely. There are many ways to do this. Many people prefer the 'Cone Method'. More information on this method can be found at this site. Aside from fresher, healthier meat, one reason people commonly raise and kill their own chickens is to make sure they live and die humanely.