Reputation
Reputation is specific to a card.
It is a reward related to PVP activity.
At first it is a zero sum currency with cards possibly losing reputation as much as others gained it between players.
It also has other benefits: it can attract periodic rewards and allow you to gain more advantages in specific game modes.
For the Conquest of Achea game mode, the more Reputation stored on your cards you have at the beginning of a season, the more individual Achean quests you will also receive as a bonus.
Reputation Ranks
At the end of a PVP season once you gain a new upper Reputation on a card, it can also unlock a new Reputation Rank.
Reputation Ranks give you a base reputation score you cannot get below.
It helps in going forward in reputation: you can't go below a certain amount so you can only “go up” from there, you can start higher than before, and thanks to more reputation at the beginning of a season you will also unlock more Achean quests and more Season Rewards.
And implicitly, even more reputation to gain from this activity too!