What does it mean exactly, to “build a statistical model” of, say, a series of images?

So this is a straight forward question, I would like to know, what it means exactly, when someone says "We built a statistical model of all our images".

I overheard this, (and keep overhearing that phrase), but I am not sure how/what that entails exactly.

What does it mean, for someone to 'build a statistical model'?

Thanks

EDIT: I am very well aware of regression, PCA, EM algorithm, GMMs, etc etc. When I hear "statistical model", I think "Ok, he has a PDF". This is what I am trying to confirm/deny. Does "building a statistical model" mean "I came up with a new PDF", or does it mean "We figured out parameters of a given PDF", or what? This is what I am trying to determine. Literally, you have a set of images, you state, "I built a statistical model"... what does that mean exactly? What do you have now?