That's called an "Articulated Matte", where an artist will literally draw round the edge of the object they want removed and then paint the inside black, creating a 'Background matte'. Then they can make a negative of that image to create the 'Cover Matte'. (And yes, they will do it for every single frame!) The process shown in this video is called a "Travelling matte", which essentially generates an 'Articulated Matte' automatically through the use of blue screen and film processing. It's amazing what they used to do before computers.
Sometimes we still do that, although it is much more streamlined and precise when you do it digitally in, say, After Effects or Nuke. It's also called rotoscoping. It is still a tedious frame by frame process, but the tools allow for much cleaner masking with soft edges for hair and fur. Old school chemical/film blue screen got better in the seventies (Star Wars, 1941) but some of the earlier attempts don't hold up so well by today's standards.
Jon Erland is a true genius. Could we get videos on the Blue Max front projection bluescreen system and the reverse-bluescreen system he created for FIREFOX (1982)?
