Your personal Libraries include the corresponding Public folders (Pictures, Videos, etc.). A Library is not another copy of a file/folder, but a collection of ones you include
in that Library. See here.
Note that the Documents Library is different from the regular Documents folder, as you can include anything in the Library but actually have to move something into your Documents for it to show up there.
And deleting the Public folder will do no good, as the files will just come back. Believe me, I've tried. They don't take up much space, so I wouldn't worry about it if I were you.