What exactly is AVAHI?

Avahi is a system which facilitates service discovery on a local network via the mDNS/DNS-SD protocol suite. More information here.

As Iain said Avahi provides similar functionality to Bonjour or Rendezvous for Linux. On a server I really don't see a need for it... I've turned it off myself on servers I've setup.

You can stop the service and then turn it off at boot using these two commands:

service avahi-daemon stop 
chkconfig avahi-daemon off