From the manual you evidentally didn't find (perldoc) :-)
in reply to Split ( ) is Giving Me a Splitting Headache
In your case, you're only passing in a single argument to split. Perl interprets this as /PATTERN/ and implicitly uses $_ as the EXPR. Since $_ hasn't been initialzed yet (hence the warning) nothing really happens (it's trying to split an undefined value on occurences of "Hello World").
perldoc -f split
What you need to do (besides taking a look at the perldoc entry for split) is use the two-argument usage of split:
my $Phrase = "Hello World";
my @Parts = split(/ /, $Phrase); # split $Phrase on spaces