
A side story is, literally that, a story that exist alongside the main story. It can be parallel (taking place at the same time), be set before the main story, or be set after the main story.
To give some examples,
Fire Emblem Gaiden is the second Fire Emblem game, it takes places in the same world and at the same time as the original Fire Emblem, and features a few characters from the original game. Another Fire Emblem game, Thracia 776, is a side story to the fourth Fire Emblem game, Seisen no Keifu, in that it covers an adventure by one of the characters from SnK at a time set during a time skip in the middle of said game.
The Lion King 1 1/2 is a side story to the original Lion King, in that it focuses on the story of side characters from the original movie. It's purpose, aside from entertainment, is to expand on the histories of Timon and Pumba. Side stories are often used in this fashion, in order to spend time fleshing out characters that didn't have enough time allotted to them in the original work.
Rhett Butler's People is a side story to Gone With the Wind that goes through much of the original story from the perspective of Rhett, rather than Scarlet.
A personal favorite of mine, Boston Legal, is both a side story and a spinoff of The Practice. Note that spinoffs and side stories are not mutually exclusive. This will be important later. Another example in the same vein as this one would be Batman: The Animated Series, and it's spinoff, Batman Beyond.
You may be wondering how any of this relates to Dragon Ball. Well, it all comes from a single quote by Akira Toriyama, where he states that he considers Dragon Ball GT to be "A Grand Side Story."

Given GT's place in the timeline, it would obviously fall into the same category of side story as Boston Legal and Batman Beyond.
The issue I see is that this statement is often used to discount GT as "non-canon." Without getting into the messier details about Dragon Ball canon, I would like to elaborate on why this viewpoint is incorrect.
First off, the problem of dealing in absolutes. When making an absolute your argument, all it requires is one contradiction to make the entire argument fall apart. Saying that GT is a side story, and because it is a side story, it is not canon, is making the assertion that side stories are, as a whole, not canon.
As a rebuttal to this, I present my evidence. All of the side stories I listed above are considered canon to their respective franchises. Therefore, saying that "GT cannot be canon because it is a side story" is faulty logic as, by their nature, side stories are not inherently non-canon to their respective franchises.
Second, there is the argument that Toriyama called GT a side story because he didn't like it, and that this somehow makes it non-canon.
Well, firstly, Toriyama's likes and dislikes don't really matter when determining canonicity, as he is not the sole rights holder. Second, being labeled a side story is not, and has never been, a sign of disdain for something. Third, he refers to it as a "Grand" side story, which doesn't really sound like an admonition against it.
So, in short, GT being a side story does not make it "not canon," nor does it mean that Toriyama dislikes the series. There are plenty of other arguments to make against GT's canonicity (as it stands in Dragon Ball), but this is not one of them.