From the Super Mario Wiki
Continue Points are items found in the Game Boy game Donkey Kong Land. They are checkpoints found at least once in every level of the game, replacing the Star Barrels from Donkey Kong Country. They appear to be mirrors that have stars shining on them, and once touched, they turn around and a thumbs-upped hand appears on them.
Donkey Kong Land bio
These sparkling circles indicate a continue point. If you make it to one of these, this is where you will continue the current level should you lose a life before you reach the end.