Galois categories are introduced (for the first time?) in SGA1, but here's an English introduction that's available online: http://www.math.uchicago.edu/~may/VIGRE/VIGRE2009/REUPapers/Lynn.pdf
It seems that Galois Categories are a way of axiomatizing all the Galois correspondences in the various fields: Galois theory for fields, Galois theory for covers, Galois theory tame covers and so forth.
What is the benefit, if at all, of this formalism? Is it just to outline the commonalities of these seemingly different topics, or is there some applicable virtue to this language?