Prestige is how well respected the ruler or the citizens of the kingdom is. Prestige is sometimes used as a social currency similar to how Piety is a currency spent on deities. Some buildings and effects increase or decrease prestige, however included here are methods and ways to spend prestige.
This can be used once every 3 turns (or in other words, once every three months); a holiday can be celebrated for one or more reasons. This could be a religious holiday (such as the birth of a saint) or a political event (such as celebrating a kingdom's founding), when celebrating this holiday you spend 10 Prestige and designate a single settlement within your kingdom. That settlement produces double Trading Assets, and doesn't incur upkeep this turn (refunding any upkeep having already been spent on this settlement if spent).
This can be used against a kingdom who is within 6 squares of you; by using propaganda and elements of espionage you are able to sow dissent among the nobles and/or peasantry, making a revolt a dangerously likely outcome. You can spend a number of prestige up to your Intrigue + 1 in order to cause the target kingdom to take a hit to their Unrest. This increases the kingdom's Unrest by an amount equal to double what you end up spending.