The term originates from the basic inventory of the company being the "property" of the owner.
General use is to give authenticity to a performance by adding a prop to give the actor "business". Interacting with a brush, sitting at a dressing table in a scene sets up the "suspension of disbelief" along with sets and costuming.
Props, short for Propers, -Don't forget that the entire word "propers" is used in the song "Respect", written by Otis Redding and most famously recorded by Aretha Franklin in 1967. At least, I think it is ("all I'm askin' in return honey is to give me my propers when I get home")-