Inferring from my native German I would say whenever you mean to express that the whole amount is being eaten so that nothing is left.
- "Jeg spiser opp pastaen" - "I finish the pasta / I eat all the pasta".
- "Har du spist opp?" - "Have you finished your plate / Have you eaten everything? [literally: Have you eaten up?]".
Can someone confirm?
It basically has the same meaning in English too, but we say "eat up" often to emphasize eat fast or with zeal. If I said "Eat up!", I would be saying, stop taking your time and finish eating, or dig in, depending on the context. We don't like taking our time to eat in America :)