But for whatever reason, FW devs decided to use the concept of tuple where other devs/engineers have not chosen to use it so much (excepting perhaps relational DB types). An n-tuple is a shopping list with n items on it, listed in some meaningful order if we follow a stricter definition. If the word itself puzzles you, think quintuplet.

Regarding firewalls, an ordered list of rules is an amazingly useful thing when playing deny/allow with multiple sorts of incoming traffic. More than five rules to sort traffic is, put mildly, way past due. Actually, there have been more than five tuples in all sorts of firewalls forever, so I don't know what these "Next Gen" vendors are actually providing here. Better configuration? More flexible? Haz DB of o-fishilly okeydokey applicashunz so zero-conf-4-u? Or maybe the additional tuples can be moved up the list more effectively, as opposed to, say, existing only in port forwarding settings, making it more effective with apps using HTTP 80. The malware filtering itself sounds just like any other AV/AM solution. I can only assume the filtering is better, more-flexible, and more all-in-one in a single commercial device than what has come before.

But tuple is just another bit of mathematical jargon used appropriately in the heavily maths-orientated world of information technology.