The license enables you to decode and encode (where applicable) the mentioned media types using the built in hardware encoders/decoders.
Hardware en/decoders are much faster and do not rely on the core CPU to process these files; rather the GPU is used to process the files. It talks directly to the Video Memory (decoding) or RAM (encoding) making it nice and smooth. You do not need this license and can use software versions. But it is really slow.
The license will be a file you place somewhere or a key you define as a global variable for the system. The en/decoder libraries will request these and pass them into the hardware where they will be resolved on that chip; if the key matches the serial number and is valid you will be allowed to use the exposed API (I can see this getting hacked very quickly).
Raspberry Pi did not include this to keep costs down. For us, a few quid is ok, but if they made a million units that is £3.6million extra they have to spend on something only a fraction of people will use.