A more thorough explanation:

A postman is a term used in the past to refer to a barrister in the Court of Exchequer who had priority in making motions. The name "postman" comes from the post he stood next to when making motions.

For example, in the Court of Exchequer, the postman had precedence in motions over all other junior barristers. This means that when there were multiple barristers making motions, the postman would be heard first.

The term "postman" is no longer used in this context and has been replaced by other terms.