What "jailbreaking" is: you download software that exploits a security vulnerability in iOS in order to write new code that allows you to also run "unofficial" (and, let's be clear here, potentially dangerous) apps on the phone.
Pros and Cons: I jailbroke my original iPhone (after the warranty and contract were up) to enable support for Bluetooth stereo headphones (Apple had not enabled it, probably due to battery drain) and take (very bad, but functional) video with it. So there are some nifty things you can do with unofficial apps, but mostly people seem to jailbreak because of some unfulfilled need to customize. That's all the app you're describing does -- makes iOS LOOK like Lion. It doesn't actually change the OS, just the looks and functionality a bit. I have used something similar (whited00r) to make my original iPhone (which I wasn't using anymore because it's limited to iOS 3.1.3) LOOK like its running iOS 5. I also had to jailbreak it in order to "unlock" it (allow the iPhone to use any GMS sim card) when I moved to Canada.
The cons are that you void the warranty if there is any. If the phone breaks and you can't get it back to factory state, Apple won't fix it for you. Another down point is that jailbroken phones are noticeably less stable, sometimes a bit slower as well, than non-jailbroken. While there's not been any serious security risks to appear so far, the POTENTIAL of malware on a jailbroken device is very high. Luckily the Mac/iOS community is strong and well-informed, or we'd be like those poor Android suckers. You may also discover that some unofficial apps (particularly if you're using a backgrounder) may end up using a LOT more data than you thought.
I can't recommend jailbreaking for under-contract or in-warranty iPhones due to the risks. Off-contract, out-of-warranty iPhones, sure if you want.
