Handshake domains work just like the centralized ICANN domain system, with a few key exceptions. In the traditional world of domains, extensions such as "com" "net" and "org" are referred to as Generic Top Level Domains or top-level domains. There are also new top-level domains like .pizza or .business, and Country Code top-level domains like .io (Indian Ocean) or .ly (Libya). ICANN decides, through an expensive and complicated auction and voting process, what top level domains will be approved, and then individual domain registrars who own those top-level domains get to sell access to the subdomains on top of them.
On Handshake, anyone can register a new top-level domain and sell access to subdomains without having to ask for anyone else's permission! For example, if you registered "lee" on Handshake, then say Bruce Lee could come and buy bruce.lee from you! However, because anyone can register a top-level domain on Handshake, another option is to simply USE top-level domains as-is. For example, Bruce Lee could just register "brucelee" and use it to host his personal website without any subdomains.