what does first run mean?

Answer 1

A "First Run" movie is playing in theaters in its initial release. Tickets are full-price.

Once a movie is in discount theaters, on video or being broadcast, it is no longer a "first run" product.

I've also heard the term used to describe the first production of things like textiles and consumer goods.

Answer 2

chocolahoma's answer is good stuff. I think the term might have come from distilling booze. Or, perhaps, printing.