My experiences up to now.

• I usually use broker.mqtt-dashboard.com as a public MQTT broker
• For local tests i use eclipse mqtt docker image

Using the default setup both do not require authentification. That makes testing pretty easy.

TL;DR

• start broker
• terminal 1: subscribe to topic
• terminal 2: publish message to same topic
• check subscriber in terminal 1 has received the published message

There're 3 components involved:

1. MQTT broker
2. MQTT publisher
3. MQTT subscriber

The general idea is one can publish messages to server on a certain topic and someone else can subscribe to a topic and is receives those messages as they arrive.

ad 1) A broker is responsible for