broker
The server in the middle that receives every published message and hands copies to subscribers.
An MQTT broker accepts client connections, keeps each client's subscriptions and session, stores retained messages, and routes every publish to the matching subscribers.
Examples
The greenhouse node and the phone app never connect to each other; each opens one outgoing connection to Mosquitto, which passes the readings between them.
Mosquitto, installed in Chapter 0, is a broker: a sensor publishes a temperature once and the broker hands a copy to every program that asked for it.
See also