What is the purpose of the §/± key on a UK Mac keyboard?
I think only Apple knows the answer to this.  

The § and ± characters are available on the US keyboard at option 6 and option-shift =.

I believe a historical antecedent for the ± key can be found in the IBM Selectric 3 keyboard.

Other Apple hardware keyboards with the same key in the same place are Arabic, Bulgarian, Czech, Dutch, English International, Greek, Hebrew, Portuguese, Romanian, Russian, and Turkish.  I suspect their users also wonder why Apple gave these two characters such status.

A much bigger mystery in my view is why the Apple British keyboard puts the " and @ characters at different places than any normal British keyboard does.  Apple eventually had to provide a "British PC" option in system preferences/keyboard/input sources to accommodate all the folks who are used to the British standard.