What is CyanogenMod? CyanogenMod is a hack. It is different for different devices that run on Android operating system. CyanogenMod means modifications, which are made to the Android software.
What it really does is it gives a lot of control and power to the users of the Android devices to make several customizations that are not possible otherwise. For example, if a user installs the CyanogenMod hack, he will be able to over-clock his phone CPU to make it work faster, change the wallpaper during the startup of the device and everywhere else, and also tether the phone data with his personal computer. These are just a few of the salient features available once the hack is made.
So, what the developers really do is take the Android source code and make several modifications to it and that is what makes it more powerful and flexible.
Now, once the CyanogenMod has replaced that Android OS with its own custom and hacked version, it then would allow a host of things that the official version of Android would have prevented. Its popularity has been such since its inception, that already there are 500,000 users of CyanogenMod to date, and it is still counting. Unfortunately there has been an issue related to running Google apps on this hacked OS. But the Developers of CyanogenMod have been smart enough to find a way out of that too.
But, the developers of CyanogenMod are not interested on becoming an organization any time soon. They are just a bunch of computer programmers who love to get their hands dirty on tweaking some Android code at night after their own office work, and doing a lot of general good.