Rumors are notices displayed in the notice window just above the chat window.
They have the format:
[Notice] There is a rumor that a person in [City Name] is selling [Item Name].
[Notice] There is a rumor that a person in [Yangon] is selling [Repair Stone [IV]].
Rumors announce that a Resident NPC is selling a specific item at a fixed price in a specified town, usually far less than the going rate at the Market. When a Resident NPC is selling such items, they are announced as a Rumor in the window just above the Chat window. You will need 100% Will and a fixed amount of gold of to buy the item the Resident NPC is selling.
The Resident NPC will stay in the announced town for a set amount of time, before moving on to another town. The Resident NPC has a limited amount of items for sale. However, there is just about always some Resident NPC selling rumor items somewhere in the World of Atlantica. The biggest limitation to buying items from Resident NPCs is Will.