AMQP (Advanced Message Queuing Protocol) is a messaging protocol that enables conforming client applications to communicate with conforming messaging middleware brokers.
Messaging brokers receive messages from publishers (applications that publish them, also known as producers) and route then to consumers (applications that process them).
Since it is a network protocol, the publishers, consumers and the broker can all reside on different machines.
The AMQP model has the following view of the world: messages are published to exchanges, which are often compared to post offices or mailboxes. Exchanges then distribute message copies to queues using rules called bindings. Then the broker either deliver messages to consumers subscribed to queues, or consumers fetch/pull messages from queues on demand.
When publishing a message, publishers may specify various message attributes (message meta-data). Some of this meta-data may be used by the broker, however, the rest of it is completely opaque to the broker and is only used by applications that receive the message.
Networks are unreliable and applications may fail to process messages therefore the AMQP model has a notion of message acknowledgements: when a message is delivered to a consumer the consumer notifies the broker, either automatically or as soon as the application developer chooses to do so. When message acknowledgements are in use, a broker will only completely remove a message from a queue when it receives a notification for that message (or group of messages).
In certain situations, for example, when a message cannot be routed, messages may be returned to publishers, dropped, or, if the broker implements an extension, placed into a so-called "dead letter queue". Publishers choose how to handle situations like this by publishing messages using certain parameters.