I came across to these brackets in my music theory book of Trinity. I don't know what are these called and what they exactly do in this music?

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These brackets indicate a "first and second ending." The measures under the "1" are to be played the first time through and those under the "2" are to be played the second time.

It's a nice method of notation and can be extended to more choices. There are also things like "dal segno" and "al fine" and others. You should check them out; search the internet for music notation.

This link has a nice summary of the most basic repeats and endings.

  • 3
    Maybe you should add they're called "voltas", since it's still used. And more specifically prima volta and seconda volta
    – Creynders
    Sep 18 '19 at 12:30
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    @DanielSank yeah but it's funnier this way. Sep 18 '19 at 12:59
  • @Creynders Just be sure not to confuse with "V.S." , 'volta subito,' indicating you better turn the page quick :-) Sep 18 '19 at 13:00
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    @CarlWitthoft "volti subito". Volti mean turn. It's also the nickname of my electrician. Sep 18 '19 at 14:52
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    Italian speaker here. Volta means may things, among whose [an] arched ceiling, [you] turn, [this] time. Volta subito: turn now. Prima volta: first time. Seconda volta: second time. By the way, Dal Segno means literally "from the sign" (da+il segno), Dal Capo: from the beginning, and Al Coda: to the "tail" = end.
    – Zachiel
    Sep 18 '19 at 18:26

The name is volta brackets. Used to mark alternate endings used in conjunction with repeat sign barlines.

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