The answer is a fairly simple one. In medieval times, small travelling theatre companies would form and travel across much of Europe putting on shows of all different magnitudes. For these shows, they would need items that would contribute to the authenticity of the piece. These were things that were everyday items, or perhaps even more obscure objects that contributed their own major or minor impact to the piece.
These items, whether bought, supplied by an outsider, or supplied by the actors themselves, would become ‘company properties.’ This was eventually shortened to ‘properties,’ which in turn the lazy people we are, we ultimately rendered them as ‘props.’
Property Masters are the people in charge of all the props for a production, whether it be stage or film. The history of the use of the word ‘master’ is slightly less clear cut, since most of the other units would have the term director or ‘head of’ attached to their title. Some people believe it could be a throw back to the old English guild system, but whether this is true or not is up for debate.
Prop hire is now a major business as the authenticity needed in productions for stage or film is much more important than it might have previously been. With more educated audiences and an array of people ready to blog about anachronisms or incongruities, getting accurate props is no longer as simple as buying something that just looks the part. Prop hire helps Prop Masters get the most out of their properties, ensuring the accuracy of everything from period to style to likely cost of such an object can be married up effectively and at much lower costs.