What it's for
Port 4369 is used by EPMD (Erlang Port Mapper Daemon), a small helper service that's part of the Erlang runtime. Since RabbitMQ is itself built on Erlang, EPMD runs alongside it in any clustered RabbitMQ deployment, helping nodes discover which port each other node's Erlang runtime is actually listening on for internal cluster communication.
Protocol basics
EPMD runs over TCP and functions essentially as a local name-to-port lookup service for Erlang nodes on a host — when one clustered node wants to talk to another, it first asks EPMD on port 4369 which actual port that node's Erlang distribution protocol is using, since that can vary. This is purely internal cluster-coordination infrastructure; application clients never interact with EPMD directly, and it should be restricted to the private network your RabbitMQ (or other Erlang-based clustered service) cluster runs on.