Those little grey circles are checkpoint discs. They bounce up and down until touched, then they disappear and set the current checkpoint.
For as long as you have lives left, when you die and the level restarts, you begin at the most recently collected checkpoint spot and any enemies already killed are gone, as well as any pickups already collected.
If you run out of lives or exit the level via the menu then come back in again, everything is reset to normal.
This makes the lives system make a bit more sense now. Only thing left is to make the word "CHECKPOINT" appear on the screen when you get the checkpoint disc, as it is not too clear what it does otherwise.