Funny thing about Danish (the pastry) is: it isn't really that Danish...
At some point in the early 20th century there was a strike among the Danish bakers. Seeing possibilities for a career many foreign bakers immigrated to Denmark. In one small bakery in Copenhagen worked an apprentice baker recently immigrated from Vienna. One day, it is said, he had forgotten to add butter to the dough of the tea cakes he was making.
A popular cake in the Turkish area of the old Ottoman Empire was the Baklava, square and made from layers of dough and butter and served in syrup. Since the whole of the Balkans was part of the Ottoman Empire for almost halv a millennia much of the Turkish culture spread all the way up to Vienna.
The bakerboy, having seen this Turkish cake solved the butter-in-the-dough problem by applying the butter on top of the flat dough, and then fold the whole thing. The new creation proved to be a success and quickly got the name Wienerbrød, Vienna-bread, after the bakerboy.
In Scandinavia it is still called Wienerbrød, but in the German-speaking world it got the name Kopenhagener Gebäck. After all; it was baked in Copenhagen! The English-speaking world followed this idea and started calling it Danish (Copenhagen is the capital of Denmark, as you probably know). Hence the name issue.
The ideal Danish is made up of 24 layers of dough with 23 layers of butter in between. It doesn't require as much counting as one may think: you simply make three layers of dough and butter and fold it three times. Voila: 24!
The first one being intended to become a tea cake, the typical danish is round and flat. But of course there are variations. It is normally filled with some sort of sweets; chocolate, vanilla créme, icing of varying colours and flavours, fruits or berries et cetera.
Over time the Danish has become something of a national flavour of Denmark, alongside the Smørrebrød and the beer. Should you visit Copenhagen at some point in your life I advice you to take a walk down to Nyhavn, enter a small café, buy a Danish and a cup of coffee and savour the moment in the sunny harbour.