In computers, stateless is the condition of having no previous data to address. One great example is HTTP, which uses a stateless protocol; meaning that the server receives requests as individual, unrelated queries and does not retain any session or status information.
There is also a stateless firewall, which does not retain any information about previously sent or received packets. The firewall doesn't know if any given packet was part of an existing connection, is attempting to make a new connection, or is rogue. Due to this, stateless firewalls are vulnerable to spoofing attacks. An example of a stateless firewall is FTP (File Transfer Protocol).