Fibrations are part of a model structure.
http://ncatlab.org/nlab/show/fibration+of+simplicial+sets
Fibrations (trivial cofibrations) are closed under pullbacks.
A variety of different notions of fibration can be found in HTT
http://www.ncatlab.org/nlab/show/fibrations+of+quasi-categories
nLab on Grothendieck fibration
http://ncatlab.org/nlab/show/fibration+sequence
http://mathoverflow.net/questions/49759/definition-of-fibration-in-algebraic-geometry
nLab page on Fibration