What are the main advantages of Kerberos?

Its messages resist eavesdropping and replay, client-service traffic can be encrypted, client and service can verify each other's identity, it supports single sign-on, and it works over insecure networks.

• Protected against eavesdropping and replay: passwords never cross the network, tickets and keys are encrypted, and authenticators carry timestamps checked against a replay cache.
• Encrypted client-service communication: phase 3 leaves both sides with a shared service session key that can protect the application traffic.
• Mutual authentication: the service proves itself with its own authenticator, so the client knows it is not talking to an impostor.
• Single sign-on: one logon, then tickets for every service in the realm.
• Works over untrusted networks: security comes from cryptography, not from trusting the wire.

On top, it needs only symmetric cryptography and relieves services of storing user passwords: each service holds just its own key.

Go deeper:

• MIT: Designing an Authentication System, a Dialogue in Four Scenes — shows how each advantage comes from a concrete design decision.