The Packet Forwarding Engine (PFE) primarily focuses on data plane activities in routing devices. It uses Layer 2 and Layer 3 forwarding tables to direct traffic towards its intended destination. Additionally, the PFE is tasked with implementing different network services like policing, stateless firewall filtering, and class of service. Functions related to handling chassis components processes and performing protocol updates and system management are managed by the Routing Engine (RE), not the PFE.