Whenever a friend starts to play this game, they can enter your Invite Code after creating their account. When they do, they are rewarded with 1 Astronomer Lorelei and you get an additional Friend Invited number (FI#). You can also get rewards based on how high your FI# is.
1 FI# = Astronomer Loreilei.
5 FI# = Daring Hasina
10 FI# = Armored Xara
30 FI# = Quick-silver Marcy
50 FI# = Small Whirlwind Malina
So in order to get ALL rewards, you should try to get 50 friends to play this game!
Hope this cleared things up for you