Notoriety is a new stat which each character accumulates, starting from 0.
The value of the stat will seldom, if ever, be revealed to the player. Instead, the player will get a sense of its value through interaction with the universe.
Notoriety translates, simply, into how known you are for various activities. It can effect how people react to you, your rights, whether you are a wanted man, or whether it’s particularly easy for you to slip by undetected.
It can also make various activities easier or harder to partake in.
For example, it is easier to shop when you’re not being hunted for killing babies, but maybe you’ll get a better deal if you’re known for killing shop keepers who don’t cooperate?