The FAA and Eurocontrol web sites are good sources for information about Mode S.
The Mode S address is 24 bits long which means there are over 16 million possible values, enough to perminently allocate one to each aircraft. The addesses are allocated in blocks to each country, the US having the largest allocation! The full list of the country allocations is in ICAO Annex 10. It is then up to each registering authority to allocate the addresses to individual aircraft.
The Mode S address is fundamental to the way the Mode S (selective) radar system works. For example, an interrogation from the ground will contain the Mode S address of the target aircraft and it will only reply if the address matches.
Hope this helps
RR