I know what the logo and icon are, but what is the banner for? And is there dimensions for it to create one?

A banner is kind of a background picture which is shown at the upper portion of the screen, but is overridden in case you have in your theme a background picture. As far as I know every image source on sr.c (logo, icons, trophy icons) is resized to its "true" dimensions, so banners will probably behave the same. If you have a background picture then that is not relevant anyway.