They're just meant to provide a bit of structured, goal oriented play. On the left side of the screen, the three little boxes; the first one gives you your limits - a limited number of moves, or a countdown timer. The second box gives your goals - a certain kind of flowers you need to collect, or birdcages you need to open, or a score you need to reach. Then the bottom box gives you your current score.
So the level is a "success" if you meet the goal within the restriction, and a "fail" if you don't.
There does seem to be a bug where sometimes the score comes up as negative. We think it's wrapping around or something, but that shouldn't effect pass/fail, it should only effect the number of leaves you get colored in on the menu screen.