Android :: Internal Memory And External Storage

I've started seeing some apps that offer to read/write data to the internal phone memory (like Super KO Boxing 2, which offers to save a whopping 52MB to the phone memory). I suppose this is because newer Android devices have a lot of internal storage, as opposed to my devices, which have very little. I would like to support internal storage in my app as well.

But it's a bit difficult to implement a solution to something that I don't really know how it works. For example, do these newer devices allow users to upload files to the internal memory, like it's possible to do with the SD card? Can someone explain internal storage from an user perspective and recommend strategies for supporting read/write operations both for internal and external memory (ie: letting the user choose which memory to use at startup, like the Super KO Boxing 2 app)?