rooting gives you access to the root user (dah!) it basically allows you to modify the entire system. For example you can remount the /system partition to delete apps.
A ROM is an entire operating system that you install in your phone and it replaces your default HTC operating system (normally along with clockwork recovery which is a backup/recovert/installing tool). you can find many roms for many phones. Cyanogenmod is the most popular one. It is very nice but it does not include sense (so you would loose any sense based app like the nice dialer). you can also find some modified Sense roms. these might not be entirely legal (not sure about this) but you can find them normally in sites like xda-developers.
Sense is not a rom, it is a framework that HTC uses to create a very specific look and feel for applications. you can only find it (legaly) in htc phones