There are a couple of reasons.
The first one is because some objects use resources other than memory, which it is important to return to the system as soon as possible so that they can be reused for other purposes. Some of these may be local to you application, others may be local to your whole PC. If they are not released, then "leaks" occur because the total number of available resources drops each time you create an instance, and sooner or later the system runs out. Since the Garbage Collector is only activated by low memory, there is no mechanism for returning these resources other than explicit Disposal. Such objects include (but are not limited to) Graphics contexts, Pens and SqlConnection / SqlCommand objects.
It also helps to free up files which are held open by some commands: Bitmap.FromFile for example aquires a write lock on the file which is only released when the bitmap is disposed. Since you can't rrely on teh GC kicking in at any point, Disposing of the bitmap is the only way to free up the file it is based on for writing.
It also helps because it can keep the memory footprint down - if you constantly allocate and Dispose objects of the same size, the same memory can be re-used and your whole app runs more smoothly because the GC is never needed (and it always runs at the most awkward times