Punycode is the ASCII encoding system that lets you register and use domain names in non-Latin scripts—Chinese, Cyrillic, Arabic, whatever—on the DNS, which was built for ASCII only. It converts Unicode characters into a string starting with "xn--" that the DNS can actually handle.
Why it matters: IDNs (Internationalized Domain Names) are real domains in real markets. Punycode is how they work technically. You register "münchen.de" but it becomes "xn--mnchen-3ya.de" under the hood. Your browser shows you the pretty version; the DNS gets the punycode version.
Relevant here: Some registries and registrars are sloppy about IDN support or add fees. We support punycode domains on most TLDs. Also, homograph attacks exploit punycode—registering lookalike domains in different scripts to phish users. ICANN's confusability rules try to block the worst cases, but enforcement is patchy.
If you want to register in your native script, expect standard registration. If you're buying as an investment or defensive measure, watch for variant strings and character-set collisions.