Goal and Stage End
It's common to have a little goal game at the end of each level or stage in Kirby. This game, of course, continues the tradition. Now, I don't know exactly what happens, but this is what I can piece together. ie: make up on the matter.
Bell Wheel
What appears to be the goal of each level, rather than a door with stars above it or such, is a bell on a wheel. There could be other end things, but this one we know exists. Kirby has to whip the bell to ring it, have it stop, and do his happy little dance. Depending on when you lash out at the bell, you can make it stop at different points. The wheel is divided into segments with different amounts of stars on them. At the beginning (this picture), the areas with two or three stars cover half the space while the dud "no go" area is miniscule. How you get it to stop, I'm not really clear on.
Level Completion
At the end of each stage, you tally up your collection. Beads, those little gems collected, appear to be the primary goal. There are other things as well, like "chains", which I'm not certain if that's collecting strings of beads in a series or connecting techniques. My guess is the prior. Additionally, there are special treasures hidden behind chests to be found. This stage had three.
Medal Ranking
The number of beads collected in a level contributes to the level of medal earned in ranking. The more beads, the better. It starts out with a sleeping Kirby and proceeds up to bronze, silver, and finally gold. It looks like the value of the medal increases with each third of the circle completed.