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 state table, a stateful firewall can efficiently manage incoming and outgoing traffic, ensuring that only legitimate packets that are part of an established session are allowed through. This enhances security by preventing unauthorized access while allowing legitimate communication to flow smoothly.