As you progress through Mount and Blade, your character will earn more and more renown. Your character's renown is basically how well known he is throughout Calradia.
You can gain renown in a number of ways:
- Winning battles - The more the odds are stacked against you, the more renown you will earn.
- Winning Tournaments
- Completing quests/missions
Renown is important as it affects a number of things, such as whether you can join a faction. The base requirement to join a faction is 160, although this can be lowered if your relationship with the faction's king is higher. To be able to help a claimant gain control of one of the factions, you need 200 renown.