That's not exactly what it does. It's functionally the programmatic reverse of the array: push @{ $First{  $A[$_] } }, $_ for (0..$#A); Let's take it from the inside out:

$A[$_]        -- the element of @A at the current index
$First{ $A[$_] }    -- the previous line is a key in %First
@{ }            -- and the associated value is an anonymous array
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So what the code does is, loop over the number of elements of @A. (If it has ten, the loop goes from 0 to 9). For each of those indices, the value at that index becomes a key in %First, and the value is the element's index, stored in an anonymous array. We have something like this:

Elements of @A:
0    zero
1    one
2    two

Elements of %First:
zero    [ 0 ]
one    [ 1 ]
two    [ 2 ]
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While we can look something up in @A by its index, we can look up the index in %First if we know the something.

Oh, and in Perl hashes have something called auto-vivification. If you access a hash key that doesn't exist (and try to put data there), the key will be created. (Useful, once you get used to it.)