Yep, root is the name of the admin account on any unix (Android is Linux is unix) - it's the same as getting admin access on a PC.
A rom is the name we call the package of: the Linux operating system + the Android virtual machine + system apps and your apps that run in that Android virtual machine, and that machine uses services from the Linux operating system.
Linux includes a kernel, just like any OS - Windows or Mac OS X or whatever. Yep, the kernel ties the hardware and software together.
All roms therefore include a kernel, and if you follow various guidelines by their makers, you can flash a separate kernel to replace the one included in your rom.
Only flash roms known to work with - and designed specifically for your phone. Stepping outside of that box is the sure way to a brick.
The roms (and the one brand-spanking new custom kernel) are found with descriptions in this forum, with links over to where they're actually hosted, usually XDA-developers.com.
CyanogenMod rom is not ready for prime-time for us yet.
See our sticky guide at the top of this root forum - we try to keep it up to date as best we can, but we do ask patience on that.
There are several good roms out that people are enjoying, you'll find threads for them here parallel to this one.
Sense is a collection of apps, widgets and settings - some roms have full Sense, some have just a little (at this time).
Use the Regraw one-click method (we have a thread on it) if you're using Windows.
First get root, then talk to folks about how to use root tools, get a little comfy with that, and then proceed to changing roms.
Welcome to rooting!!
