There are a number of definitions of GA (Genetic Algorithm). A possible one
is

  A GA is an optimization program
  that starts with
  a population of encoded procedures,       (Creation of Life :-> )
  mutates them stochastically,              (Get cancer or so :-> )
  and uses a selection process              (Darwinism)
  to prefer the mutants with high fitness
  and perhaps a recombination process       (Make babies :-> )
  to combine properties of (preferably) the succesful mutants.

Genetic algorithms are just a special case of the more general idea of
"evolutionary computation". There is a newsgroup that is dedicated to the
field of evolutionary computation called comp.ai.genetic. It has a detailed
FAQ posting which, for instance, explains the terms "Genetic Algorithm",
"Evolutionary Programming", "Evolution Strategy", "Classifier System", and
"Genetic Programming". That FAQ also contains lots of pointers to relevant
literature, software, other sources of information, et cetera et cetera.
Please see the comp.ai.genetic FAQ for further information. 

For an entertaining introduction to evolutionary training of neural nets,
see: 

   David Fogel (2001), Blondie24: Playing at the Edge of AI, Morgan Kaufmann
   Publishers, ISBN: 1558607838 

There are other books and papers by Fogel and his colleagues listed under 
"Checkers/Draughts" in the "Games, sports, gambling" section above. 

For an extensive review, see: 

   Yao, X. (1999), "Evolving Artificial Neural Networks," Proceedings of the
   IEEE, 87, 1423-1447, http://www.cs.bham.ac.uk/~xin/journal_papers.html 

Here are some other on-line papers about evolutionary training of NNs: 

 o Backprop+GA: http://geneura.ugr.es/~pedro/G-Prop.htm 

 o LVQ+GA: http://geneura.ugr.es/g-lvq/g-lvq.html 

 o Very long chromosomes: 
   ftp://archive.cis.ohio-state.edu/pub/neuroprose/korning.nnga.ps.Z 

More URLs on genetic algorithms and NNs: 

 o Omri Weisman and Ziv Pollack's web page on "Neural Network Using Genetic
   Algorithms" at http://www.cs.bgu.ac.il/~omri/NNUGA/ 

 o Christoph M. Friedrich's web page on Evolutionary algorithms and
   Artificial Neural Networks has a bibloigraphy and links to researchers at
   http://www.tussy.uni-wh.de/~chris/gann/gann.html 

 o Andrew Gray's Hybrid Systems FAQ at the University of Otago at 
   http://divcom.otago.ac.nz:800/COM/INFOSCI/SMRL/people/andrew/publications/faq/hybrid/hybrid.htm

 o Differential Evolution: http://www.icsi.berkeley.edu/~storn/code.html 

For general information on GAs, try the links at 
http://www.shef.ac.uk/~gaipp/galinks.html and http://www.cs.unibo.it/~gaioni