What is this character for?

¬

Why?

What is it doing on my keyboard?

I mean, it looks packed with awesome but I just don’t know what I’m supposed to do with it – what is its purpose?

Update from Jeffrey Cook:

Back in the dark ages (before the were any PCs, mainframe connected
terminals like the IBM 3270 were used for data entry and programming),
IBM used ¬ (EBCDIC code 0x5F) to represent (among other thing)
negation…like we now use ! (bang); also, see wikipedia “Negation” for
an example and its general use in logic.