I would guess it is done because the owners of the old web site, business, private, whatever, do not want to lose their customers/followers.
EG if, for example bbc.co.uk were to move entirely to bbc.com, they might introduce a redirect url in the old bbc.co.uk coding to capture those users who attempt to visit the BBC via the bbc.co.uk web site, and redirect their browser to bbc.com.
How is it done? See link for some examples; http://www.wikihow.com/Redirect-a-URL
Google has many more options/examples.
There are some site that has this feature built when they move their domain to somewhere else and changed the entire URL.
How and why is this usually done ??