A firewall is a network security device that monitors incoming and outgoing traffic based on defined security rules to protect internal networks from unauthorized access. There are several types of firewalls, including packet filtering, stateful inspection, application layer, and next-generation firewalls, each with varying levels of functionality and complexity. Firewalls can be categorized as host-based or network-based, with different methodologies like static and stateful packet filtering, proxy firewalls, and application inspection providing unique advantages and disadvantages.