Continuous Hidden Markov Modeling

Question

I am writing a speaker recognition program in Matlab using Mel Frequency Cepstral Coefficients, and although I have gotten the problem to work using discrete time wrapping, I was interested in try to successfully recognize speakers using Hidden Markov Modeling (HMM). I understand how to implement a HMM for simple examples (like urn and genie), but don't understand how it pertains to my problem exactly. For instance, what are actually the hidden states that the row vectors are trying to encode? And what does it mean to model these states as Gaussian mixtures? For more information on MFCCs, it gives for each speaker a matrix of numbers, where each row corresponds to the power spectrum at one given time.