What is the difference between: Rooting, Jailbreak, ROM, Mod, etc
Is either possible, legal, contractually legit and does either damage the phone?
If you were to unlock your Android phone, this would be to allow a SIM from any provider to be used in the handset. Phones are usually locked to a provider when they are purchased (the idea being to stop you using other SIM cards after buying your phone). You can however get a sim unlock code from the network when you contract runs out. You can also buy the handsets with no contract unlocked.
Jailbreaking (or rooting as its known on Android) allows you to do a few different things, the main use seems to be either tethering (however it seems that more phones are offering this as standard), or installing a custom firmware.
One thing to mention, is rooting your phone will invalidate your warranty, so if you get stuck, you will be on your own (however there are many sites out there full of people who will help you if things go wrong). There is a small risk of bricking the phone (however there are ways to recover from this too on some handsets).
Personally I've rooted my Android device and have enjoyed playing with custom firmware and it's generally been smooth sailing (although as it takes a long time to boot after flashing a new firmware, the first time I was a bit worried :P). However, I would suggest doing a fair bit of reading around first, and only approaching this once you're sure you know what you're doing.
Hope this helps!
As I understand it, unlocking (with any phone) is allowing it to work with other carriers, as you've surmised.
In the Android world, the "correct" term for the equivalent of "jailbreaking" (which seems to be an iPhone-centric term) appears to be "rooting" (which is much more technically descriptive, anyway). Rooting, as I understand it, is gaining root access to the device, which allows you to basically do anything you can figure out how to (install custom ROMs, access previously locked-down functions such as wifi tethering, etc.).
Rooting/jailbreaking is now apparently explicitly legal, although doing some of the things that many people root to be able to do is not, if it violates your carrier's terms of service (i.e. wifi tethering).