Punycode exists to be able to use non-Latin scripts in non-supported software. So whilst I like my site http://見.香港/ I can enter http://xn--nw2a.xn--j6w193g/ if I cannot enter the Unicode original form.
Some website developers program overly defensively, for example with Google Apps you cannot use punycode domains at all due to aggressive white listing that has not updated with ICANN standards.
UPDATE: Stackoverflow now supports Unicode domain names and thus comments below are outdated. The unusual domain name is the punycode, i.e. encoded, version of Unicode for systems that do not directly support Unicode.
xn--nw2a = 見
xn--j6w193g = 香港
As of 2022/1/1, Stackoverflow has a feature that interprets punycode domains as their Unicode form in preview, but not when saved. This is not really appropriate for a code platform which may be discussing punycode, but would be fine for other sites in the exchange.
Screenshot of preview function in stackoverflow: