Boy, you just asked a big one.
Switches are perhaps the biggest single key to making plot happen in the game. (Up there with variables, but one step at a time here.)
Switches are simple on/off indicators built into the program. Once a switch is changed in a game, it stays changed until it's told to change again. Changing a switch is done with the Control Switches command (first page, top command on the right-hand column in RMXP.)
There are two common ways that a switch can be used in a game-- Conditional Branches and Event Pages. They work in very similar ways.
Conditional Branches are event commands that are classic If...Then...Else statements. IF switch 23 (Got Quest from King) is ON, THEN the guard says "Here's the way to the dungeon" and gets out of the road, ELSE nothing happens.
Event Pages are similar, but specialized-- an Event runs things on the highest-numbered page that the conditions are true for. So page one might be a guard saying "Nobody gets through here without a passport!", but page 2, which has the conditions "Switch 15 (Has a Passport)," has the guard saying "Right this way, sir" and moving out of the way when you talk to him, is the page that will activate if that switch is on.
I have neither the time nor the energy to list every possible use for switches-- they are such a basic tool in the game that it's like asking for the major uses of electricity.
However, to illustrate some examples, I'll link to a thread in which I gave a lot of screenshots illustrating a way to create a quest in the hopes that it'll be some use to somebody. (I presume it wasn't any help to the original poster in that thread, since they never replied...)
http://www.rmxp.org/forums/index.php?topic=50560.0