"Canon" is a term used by fans of anime and manga. Two characters that end up as a couple in the end of a series is considered canon. Canon can also be counted for when two characters don't end up as a couple in the end due to complications, but proclaim that they love each other anyway.
IzumixMeroko was canon in the manga but not the anime because Meroko continued to love Takuto.
A piece of work -usually in reference to literature- that was written by the original author. Spin-offs, fan fiction, and any work not written by the original author of that fictional universe is considered non-canon.
I got sad at the end of Rurouni Kenshin: Seisouhen. Good thing it took out a lot of chunks from the original plot and wasn't written by Nobuhiro Watsuki, or else it would have been considered canon. :D
Oh my GOD that Naruto fan fiction SUCKED! Thank God it wasn't canon.