Can you explain stateful inspection?

Stateful inspection, also known as dynamic packet filtering, is a firewall technology that monitors the state of active connections and uses this information to determine which network packets to allow through the firewall. Stateful inspection has largely replaced an older technology, static packet filtering. In static packet filtering, only the headers of packets are checked -- which means that an attacker can sometimes get information through the firewall simply by indicating "reply" in the header. Stateful inspection, on the other hand, analyzes packets down to the application layer. By recording session information such as IP addresses and port numbers, a dynamic packet filter can implement a much tighter security posture than a static packet filter can.