The people love to gather and cheer. Give them a place to do so with the Entertainment District. In the eyes of a Sovereign, this district is mainly a source of Income and an extra supply of lots if you don't want to fill them Racetracks and Spellcrafters. Housing units in the Entertainment garrison (silly as that sounds) will allow them to soak up the passive troop bonuses offered by the buildings.
Action - Work as Actor
Players visiting the Entertainment District can literally become players in the old sense of the word. At no material cost, your character can join the actors on stage and try their hand at performing for the public. Everyone has lines to say but on everyone can say them well. You will earn an amount of Silver Thalers according to your apparent talent (Charm and Creativity).
Main - Opera House
The Opera House is there for actors to put on plays and people to come see them. These plays aren't yet announced or individually represented but when you visit the Opera House, know that they're probably working on something. Every day this building tries it's best to sell Oysters to Peers and Exemplars, but they only sell Wine to Peers. The Entertainment District will always have a high natural Education, as this building generates a large amount of it locally. Finally, the Opera House somehow decreases training costs for Peer units housed in the Entertainment garrison. This building requires Linen and Pearls to build upkeep and upgrade.
Exclusive - Race Track
The Race Track, while a popular entertainment with the people, mainly provides set of military bonuses. Each level of each track will recruit one completely free Lancer unit to defend the Entertainment District. These probably come from local obsessives who race up and down the track until they've actually got some applicable combat skills. These buildings also increase local training speed and provide a comfortable Prosperity bonus for the district. In order to keep the races constant, this building needs Horses and Hounds to construct, tend and improve.
Linked - Spellcrafter
While the Spellcrafter can be built anywhere (but the wilderness and lots you don't own) but they work most efficiently in the Entertainment District. The Black Pearls and Familiars required for this building are not simple to get your hands on but this is also one of your few opportunities to craft Spells before the late ranks of district. This building also, incidentally, provides a significant local Education bonus and could benefit any district suffering from low Education.
Minister - Master of Revels
As the Minister of the Entertainment District, the Master of Revels is responsible for ensuring the show goes on. Plays continue to be performed in the Opera House and races continue to be run around the Race Tracks. They they have rather free discretion when it comes to building on the rest of their lots.