The term Canon refers to the source material of a given series. In the Legend of Zelda series, as well as the rest of fiction, the term refers to anything which has been established as fact by official sources, most particularly the games themselves and their manuals. It is canonical fact, for example, that all daughters born in the Royal Family of Hyrule are to be named Zelda; this was established in the backstory for Zelda II: The Adventure of Link. Some things which go against canon are regarded as non-canon, because they are not established as fact. For example it is non-canon that Link fought Mario as seen in Super Smash Bros. Brawl. The term fanon refers to any information regarding the series created by fans, and is considered non-canon.
Certain statements are regarded as canon by some players, but not by others. For instance, in an interview, Shigeru Miyamoto stated that The Legend of Zelda: Ocarina of Time comes before any of the other games chronologically. Because this has not been formally established within the games themselves, however, some players view this "fact" with a jaundiced eye.
The Legend of Zelda series is perhaps unique in that its canon has been known, at times, to contradict itself; for example, the map of Hyrule has been known to change from one game to another. This makes it difficult, if not outright impossible, for some facts to be concretely established in a manner that satisfies everyone.
Spin-off games such as Link's Crossbow Training, Freshly-Picked Tingle's Rosy Rupeeland and Color Changing Tingle's Love Balloon Trip are generally considered non-canon because they are strictly separate from the main series.