<textarea class="cleditor" name="category_description" id="category_description" rows="3"></textarea>
$("#category_description").val('');
<textarea class="cleditor" name="category_description" id="category_description" rows="3"></textarea>
$("#category_description").val('');
Try this:
$('#category_description').val('');
It seems to work fine. Are you sure jquery is loaded and you really see the textarea on your screen and not your cleditor?
If you have the cleditor on your screen, you should probably use:
$('#category_description').cleditor().clear()
This is also described in the getting started when you look in .cleditor(options) Method > cleditor Object > Methods