How to empty the message in a text area with jquery?

$('#message').html('');

You can use this method too. Because everything between the open and close tag of textarea is html code.

$('#message').val('');

Explanation (from @BalusC):
textarea is an input element with a value. You actually want to "empty" the value. So as for every other input element (input, select, textarea) you need to use element.val('');.

Also see docs