If you're ever wandering around and see a normal-looking monster with an abnormal name, you're looking at a Notorious Monster.
Notorious Monsters, or "NMs," are more difficult versions of the local fauna. They are almost always aggressive. Everyone wants to fight them because of the rare treasures they carry. If you ever see players milling about an area staring at one spot, chances are they're waiting for a particular NM to appear.
It's hard to predict when a Notorious Monster might show up. Some appear based on a timer, while others randomly show when monsters in an area are killed or when the weather changes. If you find an item that comes from an NM, learn how and when it appears, and prepare to compete against other players for it.
Beastman Seals and Burning Circles
Throughout your adventures, you're likely to come across seemingly useless items called "Beastman Seals." Do not throw these away, as these are a currency used to fight special boss battles that reward players with some of the best and most expensive equipment in the game.
Beastman Seals drop off of any monster that gives experience points. When you reach the central city, Jeuno, Beastman Seals can be traded for orbs that give access to "Burning Circle" fights, or BCs. If you defeat all the monsters in the BC, a chest will appear that contains untold treasures, so save up as many as you can.