Without influence, you will be unable take part in any aspect of political decisions, and you will be vulnerable to sabotage from other clan leaders. The amount of influence that you have will determine whether or not the nobility within a kingdom will agree with your decisions, or even listen to a proposal in the first place.
The influence system in Mount & Blade II: Bannerlord is simple, but highly important once you join a kingdom as a mercenary or vassal.
