What is the purpose of avahi on a RHEL 7 server?

Avahi is the opensource implementation of Bonjour/Zeroconf.

excerpt - http://avahi.org/

Avahi is a system which facilitates service discovery on a local network via the mDNS/DNS-SD protocol suite. This enables you to plug your laptop or computer into a network and instantly be able to view other people who you can chat with, find printers to print to or find files being shared. Compatible technology is found in Apple MacOS X (branded ​Bonjour and sometimes Zeroconf).

A more detailed description is here along with the Wikipedia article. The ArchLinux article is more useful, specifying the types of services that can benefit from Avahi.

In the past I'd generally disable it on servers, since every server I've managed in the past was explicitly told about the various resources that it needed to access.

The two big benefits of Avahi are name resolution & finding printers, but on a server, in a managed environment, it's of little value.

You may want to run the following

systemctl disable avahi-daemon.socket avahi-daemon.service 

Be aware though that the above will disable avahi only temporarily. To prevent automatic reenabling, it needs to be masked:

systemctl mask avahi-daemon.socket avahi-daemon.service 

Why, oh why do vendors build packages that force dependencies on avahi?