Common event will keep an event in the background ready to run. Say you set the weather to rain as a common event it would always rain even when you move to a different area. Including in doors. But you can control the event by setting a conditional branch, which if you set a variable for the weather will stop the rain when going in doors, as long as there is a event which triggers the stop. Common events can do many things, they're great to use. Alse, Self switches can be great to use. You can use many in one event.
Variables are like probability. If I open this chest there is 1 in 3 variable chance I can have a special item, only as long as the variable goes to 3. Set variable random between 1 to 3,. If variable is 3 the item is mine, if not try again :) This event could be a common event, and then you easily make lots of chests that use the same event. Variables are really fun, and they can be like counters, or randomly decide a given outcome, they remember stuff, they're really anything you need them to be.