<form action="demo.php" method="post">
    <textarea id="text" name="text" rows="10" spellcheck="true" ></textarea></br>
    <input type="submit" value="ОК" />
    <input type="reset" value="Очистить поле" />
</form>
<div id="text_out">

</div>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js" type="text/javascript"></script>
<script type="text/javascript">
$(document).ready(function(){
    $('form').bind('reset', function(){
        $('#text_out').text($(this).val());
    });
    $('#text').bind('input', function(){
        $('#text_out').text($(this).val());
    });
})
</script>

$('#text_out').text($(this).val());

$.post('demo.php', $('form').serialize());