IDOLiSH7 has 5 rarities. In general order from weakest to strongest, they are:
Normal (N) → Rare (R) → Star Rare (SR) → Super Star Rare (SSR) → Ultra Rare (UR)
IDOLiSH7 allows cards to Awaken from one rarity into the next. To do this, look at the Idolizing/Upgrading part of this guide. The rarity of the card also determines various aspects relating to level and training.