The grep line my @odd_digit_sum = grep digit_sum_is_odd($_), @input numbers;

passes each number into the subroutine using $_. Within the subroutine that value is assigned to $input:

my $input = shift;
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The digits of each number are then split into the array @digits

my @digits = split //, $input;
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At this point, if $input is 32; then @digits contains: ( '3', '2' ).

Those digits are then summed

$sum += $_ for @digits;
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giving 5, and then tested to see if the result is odd:

return $sum % 2;
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Which in the case of 32 is true, so true is returned to grep and grep allows that input (32) through to the results array.