What in the world is a "¬"?

I have a "¬" key on my keyboard. I have no idea what ¬ means, but it's there, right where ~ ought to be. £ is where # used to live, and the location of # appears to vary from keyboard to keyboard, but is always somewhere near Return. $ is more or less in the right location, but I cannot get used to # being its own key, no Shift required. @ and " have traded places. I use many of these characters in my passwords, where they are displayed as * which only adds to the confusion. And I'd like to know why the right-hand Alt key is labeled "Alt Gr" on all of my keyboards.