In machine learning, the latent variable z is considered as a latent pattern lying under the data, which the observer is not able to see very directly. x_i is the known data, while \phi, \mu, \Sigma are the parameter of the model. With the EM algorithm, some underlying pattern z in the data x_i can be found, along with the estimation of the parameters. The wide application of this circumstance in machine learning is what makes EM algorithm so important.
