ninja'd by Tokumaru, but as usual: Posting anyway.
You divide by 16 because that's the metatile size. You subtract the height of the status bar (32) from the screen height (240) and divide by the metatile height (16). You get 13.
You divide the screen width (256) by the metatile width (16). You get 16.
So, 16x13 is how much many bytes of RAM a screen takes up in Super Mario Bros. (According to Tepples, I haven't checked myself).
It's only related to the the possibilty of scanlines being hidden as a cause/effect thing. Super Mario Bros. probably couldn't store its "MARIO WORLD TIME" at the VERY top of the screen, because some TVs might cut it off. If there was just map up there, it wouldn't matter if it got cut off. But it wasn't, so they moved the bar down which happened to have the bonus of saving some extra RAM/ROM. Since the top of the screen is scroll locked to keep the status bar from moving, nothing solid could be put there anyway since it would look strange not scrolling.
I've said how I do it and why. We've said how Super Mario Bros. works. Decide if you like either, or come up with something that suits your own game's needs better. You should be making design decisions based on what YOU need. If Super Mario Bros. didn't need to display so much text, it could have used sprites to display its information. This would mean the top of the screen wouldn't need to be scroll locked, and it could use 16x15 screens. They made their decisions based on exactly what they wanted and needed, and you must do the same.