I found this on wikipedia and this is presumably the best and shortest explanatation I ever found about latent variable models and especially these Bayesian non-parametric models:

- The
**Chinese Restaurant Process** is often used to provide a prior distribution over assignments of objects to latent categories.
- The
**Indian buffet process** is often used to provide a prior distribution over assignments of latent binary features to objects.

From the first definition, you clearly see the construction of your prior over the space of categories. You understand that you have an infinitely sized space where all the possible combinations of categories exist and you are building a distribution over this space which will then be used as a prior for the variables describing your objects.

I let you think about the second definition, but think about an infinite collection of labels you can put or not on each object wheter it has the feature or not (and maybe my explanation is not as clear as the definition from wikipedia)