It means that you can put whatever you want on your phone, without big corporate brother having to give you the ok first. In other words, if you want an app that Apple or another company doesn't think you should have (perhaps it competes with the built in app, like Safari, or something), now you can download and install it. Whereas before jailbreaking, you are stuck with whatever Apple / other company has to officially offer, as they locked the phone down.
Another term used for jailbreaking is 'rooting' (although iDevices are usually referred to as 'jailbroken', devices referred to as 'rooted' are usually Android / WinPhone in my experience.
In a nutshell: you take control of the device that you own. Who would have thought...