That means that the source code for Android is available.
It does NOT mean that all the applications must be open source, it does not mean that every app must be able to access everything in the world.
It does not mean that the web browser on the phone can access a proprietary file format that is not compatible.
It means that the source code for the operating system itself is available and can be modified.
The FACT that Android is Open Source does give us, the users and potential users, a great deal of additional possibilities WITH THE OPERATING SYSTEM.
It does not mean that phone manufacturers or carriers have a requirement to allow us to run a custom version of Android- some make it quite difficult in fact.
It does not mean that software developers are required to open source their applications (although some do.)
It does not even mean that Google is required to open source all of THEIR applications.
Being open source does not guarantee the os is easier to use, more stable or more resistant to malware.
Being Open Source does NOT mean that it is trivial to modify the OS so that a user can remotely drive their car with their cellphone!
But there ARE a tremendous number of advantages that being open source DOES provide: since the source is open, once a device can be updated (rooting and exploits usually required- carriers and manufacturers fault, not Google) it can often be updated and extended to be able to do more and work better than it did originally. Usually this is because the custom versions of Android are based on Google's Android, not the carrier/manufacturer versions.
Yes, I use Android on phones and a tablet and I am very happy with them.
Many people are likely to be happier with iPhones and other smartphones, and I am happy they have them.
But the fact remains that at an OPERATING SYSTEM LEVEL, Android is open and Iphone is not.
On a Market level, iPhone is severely restricted and Android far less so.
There are those who claim that jailbreaking and rooting are the same- completely incorrect. Very different indeed.
Jailbreaking an iPhone is more akin to installing the Amazon Market for Android than it is to rooting.