A backstory is the background of a character before they are introduced, or is information that affects the character but does not immediately affect the story, if at all. It is basically their origin and past history.
To use a very well known PPC example, Dafydd Illian's backstory is that before he joined the PPC, he was a disguised version of Maglor in a Suefic, and was dumped into a plothole upon the appearance of Maglor, and was subsequently recruited by Agents Alex Orange and Mortic Wentway.
Backstory in a fanfic that is contradictory to canon or has been contradicted by what has already been said by an original character is a charge. The latter case may not be a charge if the backstory as presented turns out to be what actually happened and the original character is mistaken; however, a backstory that contradicts canon is always a charge.
Sometimes, in PPC missions, backstory will be delivered by Captain Exposition.