Generally, side quests are not important to the main plot, but can be fun/useful for character development.
Now, side quests generally have these flavors:
Fetch Quests: Someone wants something, you get it for them. (These quests are useful for getting money and uncommon items such as Elixir-type items.)
Chain-of-Deals: Someone wants something from Bob, Bob wants something from Alice, Alice wants something from Someone, who doesn't want Alive to have his something without getting a better something from George, who in turn wants a potato. (These quests can be played for laughs, like the example. These are useful for rare items, armors, or weapons. This one is fairly common in LoZ, where you typically get a piece of heart from someone.)
Delivery: Someone wants Bob to have something, so Someone gives you that thing. Bob will either pay you for your troubles, or send you back to Someone.
These are the most basic side-quests.
Here is a good place to read about side quests and their variations:
http://tvtropes.org/pmwiki/pmwiki.php/Main/SideQuest