Thats some nice obfued golfing! I took a few minutes to understand and translate it:

$_   = ($a*($a+1))/2;   # calculate last number in triangle
my @arr = 1..$_;        # list of all numbers in triangle

my $i;
while(@arr) {
  $i++;
  my $format = ' %' . y///c . 'd'; # y///c is a short version of lengt
+h($_)
                                   # originally in "@{[2 + 2]}" form -
+- which
                                   # creates, dereferences and stringi
+fies 
                                   # a one element array ref

  my @row = splice(@arr,0,$i);     # take $i elements off the front of
+ @arr
  printf $format x $i . $/, @row;  # print the whole row, instead of u
+sing an
                                   # explicit loop like the rest of us
}
[download]

-Blake