What is the "§" key for on an Apple keyboard?

Solution 1:

It's called the section sign. It's often used in legal documents along with the pilcrow like this "§5 ¶1" meaning "section 5 paragraph 1".

Solution 2:

The name of that glyph is section sign. Some people use it in writing to refer to sections of documents. If you don't use it, you can try remapping it to something more usefull for you.