It didn't. It is just a Germanic word that got repurposed when an English word was needed for something that would previously only have had a word in Gaelic.
It is suggested that fèileadh, earlier féile, comes from an Old Irish word related to velum meaning 'covering' but it's not very convincing.
But if you look that word up in Wiktionary then it appears to mean 'sail, cloth, awning' and to be related to English veil and web. Now it makes more sense as the original kilts were just large pieces of cloth that you wrapped round you (the fèileadh mòr as opposed to the modern skirt-like fèileadh beag).
My experience of children over the last 30 years is that they seem to think that if a piece of clothing is one thing it can't be also considered something else. They insist trainers are not shoes and caps are not hats and wraps are not skirts. I have no idea where this came from as no one thought like this when I was young. Yes it's a wrap (see definition below) but how does that stop it being a skirt?
Wikipedia defines a skirt as
the lower part of a dress or a separate outer garment that covers a person from the waist downwards.
which is actually seriously faulty, IMO, as it does not exclude trousers. Nowhere in the article does it say anything to exclude trousers. Quite a serious oversight I would say. However it does list a wrap as a type of skirt, and defines it as
Wrap or wraparound skirt
A skirt that wraps around the waist with an overlap of material.
Can anyone explain where this idea that you cannot use two terms to describe the same thing came from? It is beyond me.
They would be understood to mean the same thing. The only difference is that one is considered good English and the other is not. Why is not obvious. Since you can say both of these
I will put on a kilt
I will put a kilt on
then why can't you use both of your sentences? I have no idea. I think that the preposition at the end is the traditional version, similar to the Gaelic, but that it is slowly moving forward. Perhaps one day it will be OK to have on a kilt, but not yet.