^Pretty much just a record of when you have broken the rules.
Hypothetical Example:
A new member of Staff is assigned, myself, AC, DD, Steve and Angel are all absent from the forum and you, being you =p, start doing what you do best lol and causing havok causing the new staff member to act. If this staff member doesn't know you they may let you off with a warning, when you would truly deserve a permaban (depending on what you did). The Infractions give all members of staff the information they need on a repeat offenders previous 'crimes', it allows us to pretty much say "you were warned" or "this isn't the first time"
But, otherwise, they're just the physical result of your punishment and a reminder to staff and yourself.
Mmmm pizza