The role of firewall rules in managing network security is to define and control the flow of traffic within a network. Firewalls use a set of rules to either allow or block data packets based on predetermined security protocols, effectively acting as a barrier between trusted internal networks and untrusted external networks. By enforcing these rules, firewalls help prevent unauthorized access and protect sensitive data from cyber threats. Additionally, they can assist in monitoring traffic patterns, quickly identifying potential vulnerabilities or attacks, thereby maintaining the overall integrity and security of the network.