Automagical things are things that "just work" without explaining why, perhaps because any such explanation is over your head. :)
Maybe things that work when it's least expected...

For example:
* Modern VCRs somehow set themselves to the right time.
* Small cuts in skin eventually heal.
* sun comes up, sun goes down. repeat.

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'''AutoMagical Technology'''

In general, "automagical" implies things that actually do work ("PerfectMagic", "ItJustWorks", "SufficientlyAdvancedTechnology").
As opposed to "magical PixieDust" ("fairy-dust", "magical crypto-dust", "magical AI-dust", etc.), which implies things that merely appear to work when supported by a magician and lots of smoke and mirrors.

''There is built into any technology a sense of "magic" which is really an enabling afforded by the use of prior provision of instruments and processes. Any programmer who uses an IDE, a library, a wizard, or an API, will be using the "built-in" structures, methods, and presentations which they provide. Although one may discover the underlying components and the processes they may employ in using a "BlackBoxArchitecture", the fact that "ItWorks" is usually enough given the pressures of productivity and the philosophy and practices of reuse. In doing so, one can remove themselves farther and farther away from the task of toggling switches and manipulating registers.'' -- DonaldNoyes 20071217