To discontinue something is to stop it. If you've grown bored with the magazine you get in the mail every month, you can discontinue your subscription.
You discontinue things that you want to quit doing or otherwise want to bring to an end. A company also might discontinue a product, or stop making it — you'll be sad if a candy maker discontinues your favorite jelly beans. The word discontinue combines dis-, or "not," with continue, which comes from the Latin continuare, "join together, connect, or make continuous."