i love it when people who don't know anything about cryptography try to have a conversation about it.
let me try and break it down for you:
one of the basic problems which was dealt with many years ago in computers is this:
how do i know that a file has been successfully copied or moved from point A to point B without getting messed up in some way? the answer is math.
all computer files are "digital", meaning they are a string of binary values. these values are stored in various ways (positive or negative magnetic polarization, on/off states, reflective/non surface of optical media, etc), but these all are interpreted by the computer as 1's and 0's. there are higher structures that are imposed to make the data useable, so like a txt file will be a set of hex values each presenting a given character, plus possibly a header containing additional information about the file, but each hex value is really just a string of 1's and 0's when you get down to the lowest level.
don't get too bogged down on this point aside from understanding that all "digital" files can be interpreted many different ways, one of those ways being a really long ass number.
some smart math people figured out an algorithm that you can apply to files to get a smaller number which is relatively unique, and which will end up being totally different if even one of the bits is flipped (the smallest difference possible between two files). this is the concept of a checksum, MD5, etc, and is used for many things. think of it as a fingerprint for any file. two even SLIGHTLY different files will have totally different fingerprints. there's many ways of generating these fingerprints, and for things like MS's digital signatures a big number is used as a key in generating each file's fingerprint. as a result, your or i cannot make the same fingerprint unless we have access to that big number. this "fingerprint" number is called the digital signature and it's stuck onto the end of the Xbox executables. the system verifies that an executable is what it's supposed to be by looking at this "signature" number and the file it's stuck to and seeing if they match. if they do, it should mean that the file was properly signed by the people at MS.
this is actually a seperate issue from the "media flags", which are much easier to understand:
each piece of optical media you can stick in your computer has a low level flag on it which the computer uses to recognize what kind it is (like DVD-ROM, CD-ROM, CD-R, CD-RW, etc). this is sometimes called the "book type". you may think "a blank DVD or CD is blank, so why can't i burn it with the flag set to CD-ROM or whatever?" this is actually possible, but requires a better than normal burner (i.e. one capable of bitsetting). this is not something any normal person needs to do, so it takes some digging to find one and you will have to pay extra for it.
anyways, the executable files in both the 360 and original Xbox have a set of "flags", which are basically like on/off switches that tell the system what media that executable is supposed to be run from. this is why games on the Xbox must be patched so that the executables say "yes, i can run on a harddisk".
as noted above, changing these flags in a game's executable file would change the file, and thus invalidate the signature attached to it, requiring the executable to be re-signed.