Would like to know what $1 does?

[Gat3pm]

$regexp(%comment%,( .): (.),$1)

Got this expression from someone helping me and applied it to strings like the one below. What does the $1 do? Is there a page that lists $x and explains what it does?

Money Down The Drain: Blah, Blah, Blah (2001)

[ohrenkino]

@Gat3pm

Is there a page that lists $x and explains what it does?

Yes:

Regular Expressions – Mp3tag Documentation

and there is also a page that gives hints how to format strings like

@Gat3pm

$regexp(%comment%,( .): (.),$1)

so that they come out like
$regexp(%comment%,(.*): (.*),$1)

Hints for asking Support Requests

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[LyricsLover]

@Gat3pm

What does the $1 do?

$1 is a substitution.
From the linked tutorial:

Substitution in regex refers to the process of replacing matches of a pattern with a specified replacement string. It allows you to transform or modify text based on the matches found in the input string...
You can replace string by taking reference of the matched group using $. Use the respective matched group number e.g. $1 for first group, $2 for second and so on.