A stateful firewall is a network security device that monitors the state of active connections and makes decisions based on the context of the traffic. Unlike stateless firewalls, which treat each packet in isolation, stateful firewalls keep track of the state of network connections, allowing them to recognize and permit or deny packets based on their relationship to established connections. By maintaining a table of active connections, stateful firewalls can efficiently manage traffic and provide better security. They can identify legitimate return traffic and block unauthorized access attempts, making them a crucial component in protecting networks from various cyber threats.