Prologue/Tradition
Dai-Dai-Dai
This song contains a large choral singing of what might seem like "space filler"; repetition of a melody using only the syllable "dai". It might end up sound like "bai" or "lai", and frankly, they'd all be right! This is a very special type of song called a nigun. This is a Jewish type of song which is sometimes associated with liturgy, or just social occasions of singing together without a set song; it generally involves some free-styling. A little more about this is in the glossary, here.
Chagall's Red Jew
Important Takeaways
Tevye is introduced, as well as some of the main people in the village. However, the way that he is introduced (and those around him are introduced) describes who his social circle is, in a way that very much mattered in the Pale of Settlement, where the play is set; they are Jewish.
The prologue establishes that they dress differently from those outside of their social circle, covering their heads and wearing prayer shawls. It's also accept that they also keep "kosher homes". The other, non-Jewish, people in the village are implicitly established to not do these things.
Left is a Jewish man wearing a tallis koton, or what is likely meant by "prayer shawl" for daily wear.
Right is a couple from the Ukrainian Shtetl of Trochenbrod