There are different incarnation of the Maslov index.  The one that I  most prefer is the one propose in Arnold's paper suggested by Igor Rivin. The paper  by Cappell-Lee-Miller suggested by  Greg Friedman is also an excellent source. (These two papers  helped me understand this concept but they addressed primarilty to a mathematical audience. 


 Maslov  introduced his index  in his investigation of  asymptotics of certain oscillatory  appearing in quantization problems. I suspect this  is closest to what had in mind.  It is  sometime known as the  Hormander index.    Section 3.4 of Duistermaat's book *Fourier Integral Operators*  has a rather   efficient  description of the Maslov index.  As an aside, the operators introduced and investigated by  Maslov are special examples of Fourier integral operators.