Viewing
Scanned pictures may be written to a CD or DVD and viewed on your computer or television in a much larger format from the comfort of your armchair.
Storage
One of the big advantages of scanning your old pictures is that you can store them on CD or DVD in a fraction of the space that conventional pictures take.
Retrieval
Filing and retrieval of pictures is very much easier and considerably faster. If you use a suitable digital filing system you can access individual pictures in seconds.
Restoration
There may be many old prints, slide or negatives that have faded or suffered from a colour shift. To a certain extent these can be restored using a suitable image processing programme like Photoshop Elements or Paint Shop Pro.
Many books are available on Digital Photography and some of them are very good and informative but most of them have at most a single page on scanning your existing pictures onto your computer. This is not surprising as these books have to cover a very large range of subject matter.