How it begins ? Offcorse this can't be told for sure, but we are sure that it came with Bulgarians arrival in the Balkans, there is no evidence before that.
There are 2 main legends whitch i will express.

One of the legends about the origin of the martenitsa comes from the fact that Bulgarians relied a lot on agriculture in the past. They called the month of March “Grandma March”. She was believed to be a grumpy old lady whose constantly swinging mood would result in the typical abrupt weather changes in March

There is more than one legend ociated with the origin of the Bulgarian martenitsa, but all of them are related to the Proto-Bulgarians and the founder of the Bulgarian country – Khan Asparuh (640-701).One of the most widespread stories is about the five sons of Khan Kubrat and his only daughter, Hubba (Beauty – from bg. Хубав ). He bequeathed them the decree not to divide and protect Bulgaria. After the death of their father, the sons quickly forgot his wise counsel, and they were defeated by the Hunshire leader Han Ashina. He conquered their possessions and carried away Hubba in thrall. The brothers started looking for a new land, while their sister was waiting to hear from them. And the good news arrived with the coming of the spring, brought by a falcon. In the letter, Asparuh told her that he had found a piece of Heaven south of the Danube and would settle there. Hubba escaped, led by the falcon to whose leg was tied a white silk thread. The bird took her to the new land, but an enemy arrow hit the falcon and his blood stained the thread.After receiving the message that his sister was coming, Asparuh began to tear pieces of the white-red thread, and tied them to the hands of his soldiers, telling them: “The thread that is connecting us should never be interrupted. Let us be healthy, cheerful, happy. Let us be BULGARIANS”. It was day one, March, summer of 681.

Today Baba Marta month of march are represented by gifting martenitsa to people surrounding you, as tradition says you have to tie them by yourself in gifted people hand, as a act of respect.
Today the tradition remains in old Bulgarian territoryes when there was lated from Bulgarians and other ethnic groups. People mindset change but traditions remains, probably just to proof us that. Also tradition says if you dont wear martenitsa in march  you will have bad omen.
Here is which  countries tradition remains. I will show you one pic of first Bulgarian empire just to compare it.
Where martenitsa is used:(
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