Alternate Interpretation is a broad, unofficial term for various fanfic portrayals of canon characters.
Although keeping entirely within the bounds of canon can be difficult, if not impossible, alternate interpretation is generally used to refer to characters who are deliberately portrayed in a different way than they are in original canon work.
For example, in a direct novelization of the game Bully, Jimmy Hopkins would still be considered a canon character. It is believed that the original plot of Bully was to feature Jimmy as an antagonist. Were a fanfic author to attempt to write such a story, that version of Jimmy would be Alternate Interpretation.
As an unofficial term for a subject where there is no official term, the concept of alternate interpretation can be blurry and contentious among fanfiction authors, and individual fans of a work may disagree about whether certain portrayals stick closely enough to canon to not be considered alternate interpretation.
Types of Alternate Interpretation
Alternate timeline involves taking a canon character and writing about what happened to him before or after the events of the work. A story of Jimmy Hopkins in college or in elementary school/primary school would be alternate timeline.
Alternate universe usually depicts canon characters in a setting that is fundamentally different. A fanfic with Bullworth Academy located in Vinewood, Los Santos, would be considered alternate universe.
Most crossover fanfiction is considered a sub-category of alternate universe.