Feynman's diagrams are the lingua fraca (sp?) of much of theoretical physics. As such, hundreds of books describe and explain the diagrams.Zee's new book on QFT, F. Gross' Relativistic QM and FT, Bjorken and Drell's texts, Collins, Martin and Squires, Particle Physics and Cosmology,Gauge Theories in Particle Physics by Aitchison& Hey, QED and the Men Who Made It -- Dyson, Feynman, Schwinger and Tomonoga ( a superb book), and the master's original paper Space-Time Approach to QED, Feynman in Quantum Electrodynamics, Dover, Schwinger -- a collection of the key QED papers up to the late 50s -- all of these works, a mere drop in the bucket, cover diagrams. I'm more familiar with the older literature, but I've got to bet that over the past five years, say, 50 to 100 books have come out, dealing in one way or another with diagrams. There's plenty to keep you occupied.
Basically each diagram represents a term in perturbation theory, according to well defined rules. Note also, that Feynman diagrams are used in nonrelativistic theories -- solid state physics, nuclear phyics for example.