I'm still unsure what the SuperSU program does exactly. I thought it just acted as an invisible middleman for any root permission requests from apps and stepped in before the Android blocked them?
The SuperSU application get's notified when you make a request to use the "su" binary / executable. It (SuperSU) then checks it's database to see if the requesting program/app has already been granted permission or not to execute the su binary. If it hasn't been encountered before, it will then prompt you with a pop-up asking if you want to grant or deny permission for the requesting app/program to be given root access.
And TWRP installed OK but I really don't know what function this performs now. I thought it was the custom ROM and would show a different ROM when I rebooted. Do I now have to boot into the TWRP UI and point it towards a specific boot ROM on the SD Card or phone?
TWRP is a custom recovery and is not a custom ROM. A custom recovery allows you to install a custom ROM (among other things, of course). A custom ROM is just a version of Android that a dev has tweaked to have special features not present in the stock/factory ROM.
Typically, you would find a dev's ROM thread, carefully read and follow it's specific information / directions / instructions, download the ROM .zip file to your device, verify it's MD5 checksum on your device to make sure it transferred properly, launch your custom recovery, make a Nandroid backup, save that backup off of your device to somewhere safe, do the wipes that are indicated by the dev's ROM thread, flash the custom ROM, optionally flash the gapps (Google apps package) if necessary/relevant, and finally reboot and enjoy playing with your shiny new custom ROM.