A robot is many components, sensors, motors, planners, cameras, each often written separately and needing to exchange information constantly. Robot middleware is the connecting software that lets these parts communicate through a common system of messages, so a sensor can publish readings that any interested component receives.
This modularity means a part can be swapped or added without rewiring everything, and the same component can be reused across different robots. It is rarely seen by anyone outside the field, but it is what turns a pile of independent parts into a coordinated machine.