It means that if something is really bothering you emotionally or annoying you, then do something to lessen the stress--like punching the stuffing out of a pillow, going out for a long run to clear your head, screaming and throwing a tantrum till you're too tired to do anything else, and so forth. After you "get it out of your system," you should feel like you can move forward and get on with the rest of your life.

It means to do something that you have wanted to do for a long time but never done it.