Battle Uses
Berries are the only items Pokémon know how to use by themselves during battle. Therefore, they are mainly used for hold items, though they can be given to Pokémon on the field.
Berries main uses are for healing status problems, such as burn, freeze, or paralysis. They can also be used to restore small amounts of HP.
Planting Uses
Berries can also be used to grow berry trees. You can do this by planting them in the soil where a previous berry tree was (you can also fertilize the soil, a new feature in Diamond and Pearl). You should water the seed to begin with, and a few times after that as well. You know when the soil is dry when it turns light brown; this means it needs more water to continue growing.
After about 24 hours, assuming you've been watering it, you will have a nice and tall berry tree. Now, the number of berries you recieve depends on how often you water it. If you don't water it at all, or very seldom, it will only grow two berries. If you water it frequently, you can get three or more berries.
Also, a minor note; if you leave a grown berry unpicked for too long, it will eventually shrivel up and deteriorate on the ground. When this happens, you have a chance that it will continue to grow another tree.