To run an MQTT based application you need to host an MQTT Broker (a server). In this post I will show you several free to use, open-source brokers.
Eclipse Mosquitto

Mosquitto by eclipse.org is a lightweight MQTT broker implementation with support MQTT versions 3.1.0, 3.1.1 and version 5.0.
The software is free to dowload from:
https://mosquitto.org/download/
Installation guide:
Install Mosquitto MQTT Broker on Raspberry Pi
HiveMQ

HiveMQ is an enterprise ready MQTT broker. HiveMQ is built to address some of the key technical challenges organizations face when building new IoT applications, including
Website: https://www.hivemq.com/