Hysteron proteron is the name of a Figure of speech - in other words, it is a way of using words that is out of the ordinary. It is made of two Greek words, hysteron meaning 'later' and proteron 'first'. So hysteron proteron is an inversion: putting things in an unexpected order. This has two main uses, one rather more disapproving than the other.
In the study of literature and similar areas, it describes words being put in an unexpected order for effect. (This is what makes it a deliberate figure of speech.) Many writers vary the way they report conversation by using the construction "says he". This is an example of hysteron proteron: the usual order in English is Subject and then Verb, but here we have Verb + Subject. The effect is sometimes to is to give a slight feeling of doubt.
In the study of logic, it is used to define a fault in which the wrong term is dealt with first. This is similar to the mockery that can be made when someone accidentally says things 'the wrong way round', as when the harrassed parent says, "Oh go to sleep and go to bed." The child might feel that this was an example of hysteron proteron, wanting, naturally, to go to bed before it goes to sleep.