There are different incarnation of the Maslov index. The one that I prefer is the one proposed 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.