With the recent update, a new item was introduced in Pokemon Go: Star Piece. In previous Pokemon games this was only to get ingame money and minor other things (source). Because there is no currency as such in Pokemon Go, what can I do with it?
This new item increases all of your acquired stardust by 50% for 30 minutes per use. So basically what a lucky egg for experience is, a Star Piece is for stardust (but with 50% extra, instead of doubling it).
A Star Piece provides a 50% stardust boost for 30 minutes, similar in function to a Lucky Egg.
For reference, see the Game Master file.