Marvok chains use probability to predict stuff. Using probability can sometimes get pretty wild results, so Marvok chains try and tame things by basing the likelihood of a particular event happening next on the current event thats happening now. In a musical context, the algorithm could analyse a set of songs and calculate the probability of any particular note or phrase following another in those songs.
In practice, this means that Markov chains can generate music in a similar style to that its been trained with. But whats that 'markov order' slider doing over there - how does that affect the output? And if this generates music in a similar style to its inputs, what happens when you mix up the genres?