One of the issues people have with the iPhone is that is a black box fully controlled by Apple. For developers they control access to the API, for end users they control access to the software. If they don't like the software you submit to them (for various reasons, from "It doesn't follow our user interface guidelines" to "It uses an undocumented call in our private API" to "It duplicates features in software we provide"), they will reject the submission and you are stuck with software..
The same people say that Apple should open their iPod/iPhone/iPad like they did in the past with the Apple ][ and although I agree with them, it is not the same Apple. Just like SCO was a respected Unix implementation before it was bought by Caldera who renamed itself into SCO afterwards, Apple today is a harsh business company instead of a hackers group. Same name, different attitude.
So, what can you do about it, if the creator of the hardware wants to bake the cake, cut it and then eat it too? Leave it over to people who are much smarter than me :-)
Jailbreaking is a term based on the way third-party software on the iPhone runs: It runs in a jailed environment, where it can't access anything else except the data it has provided or downloaded itself. That keeps an iPhone safe, because if you can't access something, you can't do any damage there. By breaking the jail, you will be able to access the place where the iPhone installs software and thus install more software. Software which didn't go through the rigorious screening of Apple, software which does do things that Apple doesn't like. Google for "apple iphone jailbreak", it is not that difficult to find and works quiet well.
So, once you have jailbroken your iPhone, what do you get. Access to a different version of the App Store app called Cydia sto start with. Just like the App Store app is the way to install Apple sanctioned software, Cydia is the way to install the free software.
For the rest I have installed so far:
The iPhone can offer more than Apple is willing to show. Thanks to the hard work of a few individuals, it can be made available.