Say you want to translate a sentence from language A to language B. You have a system that generates 10 possible translations in language B. Now you use a language model of language B to figure out which is the best translation by asking the language model which of the translations has the highest probability of being generated by the model.

Chat bots, image to caption, and question answering are some more realistic use cases of the generator side. In those cases there is some input (previous chat message, an image, a question) which is encoded into a vector sometimes referred to as a context or thought vector. The decoder/generator unfolds that vector into a series of words.