In a forum, it means the thread is stuck to the top no matter what other posts are made. Normally a new post will move the thread to the top and older threads get shifted down. Stickies stay where they are. So in other words, if there is one sticky in a forum section, it will be at the top and no matter how much time goes by, it will stay there until it's unstuck.
Usually they are used for forum announcements so that everyone gets a chance to see them. Often they are used for forum rules.