Do you mean Punycode, or this joke?

Punycode? It's to allow non-ASCII characters in domain names without breaking compatibility with all the standards and software that specify that domain names only use ASCII characters.

In a lot of languages it is good to be able to render something other than us-ascii. In many places the Latin alphabet without diacritics will be well understood and no problem, but that isn't true everywhere.

There are a bunch of different human writing systems. All of them are weird because they were invented by humans, most of them are very weird indeed because they were invented by humans a long time ago and then gradually mutated.

The Latin system is the one you're using here. It's very popular. Most humans in the integrated tribes are somewhat familiar with it‡. It has twenty six "letters" and then twenty six more "capital letters" which look different but mean almost the same thing for some reason, and then a bunch more symbols that aren't quite letters although some (apostrophe, ampersand) have a better claim than others. But other popular systems include Han, which has a shitload of logograms, and Cyrillic and Greek which have different letters than Latin and different rules about how letters work.

Anyway, the people who invented DNS only or primarily used the Latin system and they weren't much into capital letters. So, their system doesn't treat capital letters as different and only has one set of twenty six Latin letters, ten digits, a dash and an underscore for some reason.

But, lots of people who do NOT have Latin as the primary or only writing system found this annoying to work with. They wanted to use their writing system with DNS especially once the Web came along and popularized the Internet.

Punycode is a way to use some reserved nonsense-looking Latin text in any DNS label to mean that actually this DNS name should be displayed as some Unicode text. Unicode encodes all popular human writing systems (and lots of unpopular ones) fairly well, so this sorts the problem out. Specifically Punycode reserves Latin names that start xn-- for this purpose. By only caring about display this avoids changing anything in the technical underpinnings. Only user-facing code needed to change, every other layer is unaltered.

The rules about IDNs say that a registry (such as .com) should have rules to ensure the names in that registry are unambigous and meaningful. But in practice the purpose of the .com registry in particular is to make as much money as possible regardless of the consequences. So you can register any name you please and they won't stop you even if it's deliberately confusing.

‡ None of the extant unintegrated tribes have writing. This probably doesn't mean anything important.

It turns out sometimes people might just want to register mañana.com or 魔法少女まどかマギカ.jp or whatever.

Imagine if DNS consisted only of Arabic characters. Imagine how grumpy you'd be that you couldn't go to newyork.gov.us for your local government website, and instead had to go to نيويورك instead?

Assuming you can't read Arabic, how on earth would you even recognise that address, let alone remember how to type it.

Unicode and Punycode were originally designed for letting computers handle the wide variety of human writing systems, common ones like Chinese and Arabic, as well as rarer ones. Much more recently, the emoji characters were added to that same Unicode system, so any encoding system these days that's international-friendly also ends up supporting emoji as well.

So Punycode wasn't specifically designed to work with emoji, it just happens to work with emoji because emoji are part of Unicode.