Pizza Box is an all purpose term used to describe a small single function server that is often used by network appliance vendors such as Infoblox, Cisco, BlueCoat, et al to deploys software applications that network teams use (because server people don’t like to share tasks, and network teams find it difficult to share responsibility). Most often these servers are OEM Dell boxes.
The term comes from the fact the the server doesn’t need a lot of horsepower, has lower specification silicon and thus lower cooling requirements. Because of this it can be reasonably small, is 19″ wide and about 20″ deep. Almost the same size as a large pizza box.
Note that pizza boxes are becoming less common / obsolete as these software applications migrate into virtual appliances on VMware.