What is the overall concept of having an iPhone Jailbroken?

Basically, it means breaking the lock on the phone that the software installed on it has. In essence your phone is just a little computer, and like any computer you can install any operating system on it you want. Where you may put an Apple OS on your PC, or vice versa, or maybe a linux…. you could put another OS on your phone, or install applications that are otherwise blocked by the apple iOS that comes installed on the phone.

The problem is that once you’ve jailbroken it, you’re completely on your own. Neither your service provider nor apple will help you with any problems you have. In fact there is some concern that Apple may use something in the user agreement to cut your service all together (something to the effect of you’re just renting your phone and don’t actually own it).

That said, tons of people have done it and do do it, without any issue. If you’re not tech savvy though I wouldn’t even attempt it.

This may be of assistance

Some people also conflate the term jailbreaking with unlocking.

Unlocking (without necessarily jailbreaking) enables you to use the phone on another network or out of your native country, while traveling, without incurring huge expense.

You can also purchase an unlocked phone (for a significantly higher cost since it’s not subsidized by a carrier).

I’ve also read recently that ATT will now unlock iPhones upon request IF the original two year contract has expired. I haven’t tested this out on my old 3G yet since I really don’t have any practical impetus to do so, but if I ever travel outside the US, I definitely would.

The other important thing to note regarding jailbreaking is that it voids your warranty.