You will find the answer to your question in "Regexp Quote-Like Operators" in perlop - basically, different regex operations have different return values in different contexts. See also perlretut for a tutorial.

my $x = "foobar"=~/[aeiou]/;  # => $x is true
my $y = "foobar"=~/[xyz]/;    # => $y is false
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my $str = "foobar";
my $x = $str=~/[aeiou]/g;
# matches first "o"  => $x is true,  pos($str) is 2
$x = $str=~/[aeiou]/g;
# matches second "o" => $x is true,  pos($str) is 3
$x = $str=~/[aeiou]/g;
# matches "a"        => $x is true,  pos($str) is 5
$x = $str=~/[aeiou]/g;
# no more matches    => $x is false, pos($str) is undef
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my ($x) = "foobar"=~/[aeiou]/;  # => $x is 1
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my ($x,$y,$z) = "foobar"=~/[aeiou]/g;
# => $x is "o", $y is "o", $z is "a"
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my ($x,$y) = "foobar"=~/([aeiou])(.)/;
# => $x is "o", $y is "o"
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my ($w,$x,$y,$z) = "foobar"=~/([aeiou])(.)/g;
# => $w is "o", $x is "o", $y is "a", $z is "r"
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my $x = "foobar";
my $y = $x=~s/[aeiou]/x/g;  # => $y is 3
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my $x = "foobar"=~s/[aeiou]/x/gr;
# => $x is "fxxbxr"
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In this table, "true" and "false" refer to Perl's notion of Truth and Falsehood. Remember not to rely on any of the capture variables like $1, $2, etc. unless the match succeeds!

In my $foo = "bar"=~/a/;, the right-hand side of the assignment ("bar"=~/a/) is in scalar context. In my ($foo) = "bar"=~/a/; or my @foo = "bar"=~/a/;, the right-hand side is in list context. That's why, in your example, you need those parens in ($value): because you want the matching operation to return the contents of the capture group.

Note that your expressions can be slightly simplified, not all the parens you showed are needed:

my ($value) = $row =~ /.*,(.*)/;
# and
$row =~ s/,[^,]*$//;
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A few additional comments on your code:

• ($row =~ s/,[^,]*$//); # gets substring before the last comma - this comment isn't quite right or at least potentially misleading, since it deletes the string before after and including the last comma.
• /.*,(.*)/ matches any comma anywhere in the string, for simple input strings it may behave correctly, but I'd strongly recommend coding more defensively and writing it like your second expression: my ($value) = $row=~/,([^,]*)$/; - the $ anchor makes sure that the regex only matches the last comma and what follows it (unless you use the /m modifier, since it changes the meaning of $).
• While the use of Scalar::Util's looks_like_number is often a good idea, note that if you don't mind being a little more restrictive, Regexp::Common (or a hand-written regex) would allow you to combine the two regular expressions:

  use Regexp::Common qw/number/;
  
  my $row = "a,b,c,d,15";
  
  if ( $row=~s/,($RE{num}{real})$// ) {
      print "matched <$1>\n";
  }
  print "row is now <$row>\n";
  
  __END__
  
  matched <15>
  row is now <a,b,c,d>
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• If this is a CSV file, consider using Text::CSV (also install Text::CSV_XS for speed)

Update: Added s///r to the table and added a few more doc links. A few other edits and updates. 2019-02-16: Added "Return Value on Failure" column to table, and a few other small updates. 2019-08-17: Updated the link to "Truth and Falsehood".