What is the purpose of using the word "automagically" when we already have "automatically"?

Solution 1:

This comes from computer jargon, and the jargon file lists it.

Automatically, but in a way that, for some reason (typically because it is too complicated, or too ugly, or perhaps even too trivial), the speaker doesn't feel like explaining to you. See magic. “The C-INTERCAL compiler generates C, then automagically invokes cc(1) to produce an executable.”

This term is quite old, going back at least to the mid-70s in jargon and probably much earlier. The word ‘automagic’ occurred in advertising (for a shirt-ironing gadget) as far back as the late 1940s.

Automagically implies certain 'magic' going on behind the scenes.

In Atwood's example it might be a bit too much or just appropriate. It depends on when it was written: today automatic updating is common, but it did not use to be. In the days when it was not common the term "automagically" fits very nicely.

It also fits well to describe the change, if the process required user action before, you can say that now it happens automagically.

Solution 2:

The meaning reported from the NOAD is the following:

(especially in relation to the operation of a computer process) automatically and in a way that seems ingenious, inexplicable, or magical.

As per the origin, the dictionary reports it's 1940s, from the blend of automatically and magically.

The meaning of the word is different from the meaning of automatically, and the word is generally used in a specific context.