If you read the Overview & Terminology page, you already know a little bit about influence and what it does. Influence has two main purposes:
As stated on the Auditioning Performers page of the game guide, every group starts with a minimum of 300 audition points. For every 100 influence you gain over 3,000, you will earn 10 more points. For example, a group with 3,900 influence would have 390 points to spend.
Event hosts will be looking to get the highest influence groups to perform at their shows. Having a high influence will often make it easier for you to get into events.
Getting More Influence
You can get more influence from the following: