It's called a "token" or their "district token"
To indicate to the network that a particular node is about to transmit data
Madge, the mayor's daughter.
District 11 sent Katniss a loaf of bread as a token of thanks and condolence after Rue's death.
yes!
As far as i can tell with researching it. There seems to currently be no purpose. it just sits there
The token indicates current "ownership" of the ring, in that only one client at a time can have access to the network. If you don't have the token you can't do anything on the network. It also indicates the status of the ring, whether it is in use, available to transmit on, health status, etc.
It takes care of mainly unimportant district issues.
So they can get money for something in their district.
District is a noun. It refers to a specific area or region, often with a specific purpose or function.
The motto of Central Independent School District is 'Pride ... Passion ... Purpose'.
That's called a "token".That's called a "token".That's called a "token".That's called a "token".