say @links looks like this:

@links =
(
    [1,2,3],
    [4,5,6],
    [7,8,9]
);
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and you apply

my @urls = map { $_->[0] } @links;
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@urls will end up as

@urls = (1,4,7);
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basically the code will produce a list that consists of the first elements of the anonymous arrays in @links.
see perlref