.HK represents the official domain extension or the internet country code top level domain (ccTLD) of Hong Kong. It was introduced in 1990 and was intended for entities with affiliation to Hong Kong. Companies wishing to use .COM.HK must go through a verification process before they can use the domain suffix.
There is no special process needed to register of a .HK domain name, all you have to do is follow the usual order process.
Popular in Hong Kong, but also used by some Russian 2ch style imageboards