Notoriety is essentially your wanted level. The higher it is, the closer to notorious you are. Notorious is the state where guards take one look at you and say "Get him!". You want to keep the symbol of a head inside the gauge white. Gaining notoriety is easy; just do criminal activities, assassinate in front of people, kill guards in general, run across rooftops, and even just bumping into some guards by accident. Losing notoriety is also easy. The game tells you the three methods of losing it: rip down posters, bribe heralds, and kill officials. The first is the easiest because those are most abundant. However, because of that, they also give the smallest returns (up to 25% of your notoriety bar per poster, or four posters if you are notorious). If you are that bad off, four posters can seem next to impossible. However, you will be jumping about a lot anyways and will be bound to find a couple of them. The second method, heralds, is your middle ground, but it comes at a price: 500 Florins for up to 50% of the notoriety bar. The cost is 1,000 Florins if you are notorious. Do not be deterred by the cost. That cost turns into a very slight profit. The last method, the officials, give the best return, but are also difficult. Like the thieves and couriers that you chase down for cash, they run everywhere once they see you (up buildings, across beams, through crowds, and most especially towards guards). The reward is 75% of the bar for an official, but the time spent could have been better used ripping down posters and bribing heralds.
If you accidentally kill someone in front of some guards, kill an archer and his body falls to the ground, or do something else that gains notoriety, this trick will allow you to get rid of up to half of it and gain some money, all without having to hunt down posters or officials. First, find a herald. He will be noisy and talking about you. Bribe the herald. He will take 500 Florins and you will lose up to 50% of maximum notoriety. If you have under that, there will be no notoriety remaining for you. Here is where this expense can be turned into a very slight profit. Pickpocket the Herald. You will gain about 3 to 5 notoriety back, maximum. This is handled easily by a poster. Most heralds have at least 3 to 5 Florins, and the money you gave them goes into their pocket, so you will gain your bribe back plus whatever they already had. It is not much, but it gets rid of the bulk of your notoriety. The useful part is, if you have anything over halfway along the first diagonal of the notoriety gauge, just use this trick and find a poster afterwards.