What does this mean?
Asset prices follow a mixture of normal distributions with a mixing process dependent on the unobservable information arrival process.
There is actually a financial example on the wikipedia page. The basic idea is that at different times asset prices are drawn from different gaussian distributions. For example, maybe sometimes (boom) asset prices are drawn from a distribution with a higher mean, and sometimes (bust) they are drawn from a distribution with a lower mean. Unfortunately, at any given time we don't know whether we are in a boom or a bust. The goal of estimating mixture models is to jointly estimate the mean and variance of the N gaussian distributions and the probability that current prices are being drawn from each of the N distributions.