Being star-ed means you will be placed on top of one's Friends list - usually means you are an important pal to them so that they could keep an eye on your status.
It also means that now you got one more stamp - "You're a Star", in your collection and could use it in your letters.
To mark someone as starred, please follow the instruction:
- Go to Friends (2nd tab, bottom menu)
- Tap a friend
- Go to More (top right corner)
- Select Mark as Starred
Unfortunately, you are not able to see who has star-ed you from the app. If you really want to know, why not ask your penpals if they have done that?