Rooting is, as Demo24 said, simply gaining administrative rights on the phone. Putting in a new ROM or kernel generally requires you to have access to a recovery mode which will allow "unsigned" installs. Recovery mode changes require an unlocked bootloader. There are some workarounds and half-measures depending on the phone/tablet (example, the Nexus line of phones are completely open, the original Motorola Droid can have it's recovery replaced, and the newer Droid 2/X can do a partial rom replacement with some trickery but not full control or replacement).
I believe the Nook Color is the most open and easily hacked tablet right now (and you can buy 3 or 4 for the price of a XOOOOM!).