Requests are tasks requested by residents, and Disney characters and café staff. There are two different types of requests.
Café Requests are requests that café staff and café customers (residents) give the player. Getting them done will allow the player's party gauge to fill faster. There is always a key request at the top of the list which is the most important request. If the player fulfills the key request, the café's level will go up or get closer to raising. There is a finite amount of key requests in a select order; once the player completes the final key request to obtain the highest café level, they won't have to complete another key request again (though regular café requests may always be completed at any time).
Favors are solids that residents and Disney Characters ask the player to return them. They usually might have to do with the player giving them an item/items, or the player modeling outfits for them. Once they are completed, they result in the player receiving a reward from the character such as an item or recipe. Sometimes, in return, the player will earn a photo opportunity with the character (only with Disney Characters).