These are mysterious enemies that invade Norende village. They can invade the village when you're updating your data via the Internet or when it is sent by other players via Streetpass. They are optional enemies and they don't do any harm in the village. However, they can reward players with considerable amount of gold, experience and job points when defeated. Nemeses sent from the server will disappear upon defeat and you have to wait for a new one to arrive again the next time you connect online. However, nemeses sent via Streetpass won't disappear so you can have a rematch again. Make sure to protect them if you want a rematch to avoid getting deleted on the next updates.
When the Nemesis icon appears in the village, touch the icon to see the options then select It is recommended to save the game first and fight only the nemeses that is within or lower than your level. Defeat means game over!
Your village can only hold up to seven nemeses at once. If the eight arrives, the oldest one will be replaced. If you want to keep a nemesis from disappearing (especially those who are around your level), you have to tap their icon and select "Protect". You can also share a nemesis via Streetpass. To do this, tap their icon and select "Send". You can even send a protected nemesis.