Explain: Latent Variable (e.g for Latent Dirichlet Allocation)

I am trying to understand the Latent Dirichlet Allocation but therefore I need the basic understanding about what exactly a latent variable is in that sense.I know that the basic idea of a latent variable is something unobserved (like an unknown parameter) that is assumed to explain an observed event.Could somebody explain to me (preferable in easy words) what exactly a latent variable is and perhaps give a simple example just to get me going?Something I'd also would like to know is if the Maximum Likelihood Estimate $\mathcal{L}(\theta;x_1,\ld...Read more