What is the badge bonus & how does it benefit a trainer??

I see the bonus metal but do trainers actually receive a benefit?? Or, is this bonus just like the metals and a trainer doesn't get anything but a metal on the web page/paper? Please explain..... Does a trainer get a Pokemon, dust, Poke coin, XP ....????
Also, does this caught Pokemon bonus include everything a trainer has caught from the day they began playing Pokemon Go? (I started August 1, 2016).
Bottom Line:. Please explain how we trainers benefit & what the actual extras are that we receive as a bonus. Thank you so much for your patience.