Notoriety is the level of fame that your Evil Genius currently holds.
The player's notoriety is the level of renown that the Evil Genius has achieved, and is gained by successfully completing Acts of Infamy on the World Map, or 1 point of notoriety every time you gloat over captured agents in their Holding Cells. Gloating over Exceptional Agents grants 2 points of notoriety.
This especially important when trying to attract Henchmen, as they are a vain bunch who only work for an Evil Genius they respect. It is also a double-edged sword as Super Agents will only become active when your notoriety reaches a certain level.