PyMQI is a Python interface to WebSphere MQ, an IBM middleware product (often called just MQ).
IBM WebSphere MQ (MQ Wikipedia page), formerly known as IBM MQSeries. is a Message-Oriented Middleware product.
I had worked for a bit on MQSeries some years earlier, on a project for a large international courier company, when I was at Infosys Technologies. It (MQSeries) was a powerful product.
Basically, it allows creating message queues and then sending and receiving messages on those queues, across machines on a (possibly worldwide) network. Messages can be sent even if the target machine is down sometimes. There is also a concept of queue managers. MQ is available on many operating systems and messages can be sent across operating systems, i.e. from OS A to OS B.
Both queues and queue managers can be accessed programmatically as well as via commands. There is support for programming MQ from different languages. I don't remember Python support being there earlier, but it is now, with PyMQI.