Hi Fallout,
Jailbreaking and unlocking are terms that are bandied around the iPhone community. People don't always take the time to explain what they are or why they are valuable to users, so we thought we'd sit down and explain why they are still beneficial to the community at large.
Jailbreak
"Jail" refers to file system limitations put in place by Apple on standard iPhones. These limitations restrict iPhone read and write access to just a small part of the media partition. You cannot access system files at all and you cannot use the disk directly as you would with an iPod with disk mode enabled.
"Jailbreaking" opens the entire iPhone file system for use. Once jailbroken, you can read and write to system files as well as media files. You'll be able to use SFTP, AFP, and other standard file access protocols to read and write data. For example, you can use a client like Cyberduck to move data onto and off from the iPhone.
Jailbreaking also allows you to install third-party software (typically via Cydia) without using App Store and to access the Unix command line via OpenSSH. This lets you install software that otherwise cannot be obtained through App Store such as MMS clients, video recorders, and more.
Unlocking
As for unlocking, most phones (here in the US, anyway) are "locked" to a particular network. In the iPhone's case, that's AT&T for the US, O2 for Great Britain, and so on. Should you want to use your iPhone with another GSM carrier, you need to unlock.
Unlocking lets you place calls with any GSM carrier by inserting different Subscriber Identity Modules (SIMs) into the phone. Normally these SIMs from unapproved carriers won't work. When your iPhone is unlocked, just buy a local GSM-compatible SIM, place it in your phone, and make your calls. You'll be able to use your iPhone around the globe without paying exorbitant roaming fees.