in lay man terms root is an act of getting "administration control" over your device.
Doing this will allow you to access system files, change the operating system and even changing how some of the hardware operates. Note that this will also break down most of the android security measures as system files etc are now accessible.
roms are like operating systems. Since android is open source, many independent developers customize it to suit their taste. Many let their custom roms open for anyone to download and use or even modify further. Every rom will have their own special features.
You are required to root your device to install a custom rom.
Leaving it at stock rom is perfectly alright. I believe most users leave their devices in stock form (and it is safer

).
I personally left my phone in stock... (and I think you can already do a lot more things than what you can on an iPhone, but both has it's pros and cons

)
If you wanna try out, I posted a step by step tutorial on rooting your device:
http://forums.hardwarezone.com.sg/79041384-post2599.html
If it's still a bit much to handle, I'm pretty sure there are 1-click root solution you can find with a google search.
But remember, rooting isn't always a good thing... and it does tend to give you some problems you need to fix along the way.. if you want a trouble-free interface, it's best to leave it at stock...
Hope that helps.