What is the difference between Stateless and Statefull firewall?

A stateful firewall (any firewall that performs stateful packet inspection) is a firewall that keeps track of the state of network connections (such as TCP streams, UDP communication) traveling across it. The firewall is programmed to distinguish legitimate packets for different types of connections. Only packets matching a known active connection will be allowed by the firewall; others will be rejected.

Stateful inspection, also referred to as Dynamic Packet Filtering, is a security feature often included in business networks.

 A stateless firewall, a firewall that treats each network frame (or packet) in isolation, was normal. Such packet filters operate at the Network Layer (layer3) and function more efficiently because they only look at the header part of a packet. A drawback of pure packet filters is that they are stateless; they have no memory of previous packets which makes them vulnerable to spoofing attacks. Such a firewall has no way of knowing if any given packet is part of an existing connection, is trying to establish a new connection, or is just a rogue packet.