As a player, your aggro radius is something you're constantly aware of when moving through a zone or area full of mobs, especially those zones of the same or a much higher level than yourself. You have to be watch your aggro radius during a raid, for the benefit of the whole raid. Woe betide anyone pulling additional mobs during a raid because they weren't watching their aggro radius. Your Raid Leader will hate you.
The term aggro radius can also be used outside of the gamer world - irl - to describe your general personal space and the annoying tendency of some people to wander into it and piss you off, which can occasionally result in a similar outcome of blood, guts and mayhem.
Raid Leader: "Watch your aggro radius, people."
Duuuuuuuudeeeeee, you moved us right near those elites and stuck them in our aggro radius...now we've got a huge corpse run arrrgghhhh!!!!111!!!!!!!!!.
This eejit is really getting in my aggro radius. It's gonna get messy if they don't back off soon.