"Desired" and "Undesired" are statuses of Treasures. Each Treasure has three values: the Undesired value (marked in red), the Standard value (marked on a coin icon), and the Desired value (marked in green). By default, the Desired and Undesired value applies at Ports with the names indicated below the Desired and Undesired values on the Treasure card. At other Ports, the Standard value applies.
Certain Traits and other effects can override the location-based decision of which value applies. For example, the SAVVY Trait allows a Crew member to sell one item at the Desired value when you Visit a Port, no matter what the name of the Port is.
Treasure
Treasure Cards represent various types of items that can be gained as Spoils, bought and sold when Visiting a Port, or used to gain the effect described on the card. Some Treasure Cards can also be handed in as if they were Clues; this is marked by a number and the Clue icon (a looking glass) near the middle of the right edge of the card.
There are many different Treasures, and they are grouped into four types: Commodity, Shanty, Trinket and Relic. All four types are handled the same in most situations, but sometimes cards or other effects may tell you to gain a particular type of Treasure. In that case, draw cards from the Treasure deck until a Treasure of the specified type is drawn. Discard the other cards drawn.
When buying or selling a Treasure, the price depends on which Port the trade is made at. Each Treasure has three prices marked on it: a Standard price marked on a coin icon at the bottom of the card, a Desired price marked on a green field to the right of the Standard price, and an Undesired price marked on a red field to the left of the Standard price. The Desired and Undesired prices have the name of a Port marked below it, meaning that price applies at that particular Port.
When you buy a Treasure, you store it in the Hold on your Ship Board. Note that the Hold has a limited capacity (by default 3 Treasures).
In addition to being possible to buy and sell, Treasures often also have some effect that can be used. The effect is described on the individual Treasure card, and usually involved discarding the Treasure after use.
If the Treasure deck runs out of cards, reshuffle the discards to make a new Treasure deck.