To slip away is to quietly leave so that no one notices. If you're not a fan of birthday cake, you might try to slip away from your friend's party before dessert is served.
You can easily slip away from an extremely boring lecture if you're sitting in the back row. Or you might plan to slip away early from a baseball game, only to get so caught up in the excitement that you end up staying for all nine innings. Another meaning of slip away is "elapse" or "go by," like when a whole summer seems to slip away, and suddenly it's September.