Backups

Gameplay
Because the game starts out in the same style as Super Mario 64, there is a notion of stars within the game. In particular these are referred to in the story as 'backups' of Nintendo games that have been corrupted.

Lore
When the game first starts out one is under the allusion that Bill Gates is the villain and that they were responsible for infecting Nintendo games with viruses that ended up creating the world the game is situated in. Because of this the backups you collect as Mario and Link are described as preserved copies of fragments of the original games before the corruption.

However, as the game reveals in Final Chapter: A Fact, Bill Gates wasn't even involved in the events of the game at all and purely served as a red herring. Furthermore, there were also no viruses as well. This leads to a bit of speculation as then there isn't anything indicating what they actual are or the purpose they serve. The only thing that can be determined is that they have some kind of connection with The Twibug due to the fact that collecting each of them causes the dome to shrink.

Trivia

 * 1) The backup Egadd has in the base at the beginning of the game has a glitch that allows it to be collected multiple times. As a result, this shows that there is no limit to the amount that they will shrink The Twibug. This has been used by speed-runners such as Pwulla.