URLs were traditionally limited to Western characters. That was a problem for people who spoke languages which used a different character set: Greek, Cyrillic, Chinese, and so on.
Allowing other character sets to appear in URLs sounds easy, but it isn’t. The problem is that it creates all sorts of new possibilities for fake websites, which can then be used in phishing emails. For example, suppose you ended up on barclayς.co.uk. Would you realise that the last letter was a Greek final sigma and not an s? There are some cases that are even worse, where there is no visual distinction between the characters at all.
To prevent this, Firefox will only show Western characters—unless the domain is registered in a country which has specific rules about the characters which are permitted. Because the UK doesn’t, if you visit the link above in Firefox, you won’t normally see Greek characters in the URL. Chrome took a different approach. Chrome will only show you characters from languages that you claim to be able to speak. If your language preferences include Greek, you will therefore see Greek characters in the URL.
If you want to see a Greek URL, therefore, it’s easiest to use Chrome. Add Greek to the language preferences, and it should just work.
There are lots of other funny traps with this. Greek has two lower case sigmas: σ and ς. There is only one upper case sigma: Σ. Because URLs are case-insensitive, this creates problems. Is πέτρος the same name as πέτροσ? The answer is yes, and in fact πέτρος will magically turn into πέτροσ, even though the latter is bad grammar.
Oh yes. πέτρος is the apostle who is normally called Peter. So πέτρος is almost my name in Biblical Greek.