<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>Document</title>
</head>
<body>
<input type="text" id="in">
<input type="submit" id="inp" value="Вставить">
<div style="" id="testD"> </div>
<script src="http://code.jquery.com/jquery-1.8.3.js"></script>
<script>
$(function() {
$('#testD').html(localStorage.getItem('testD') || '');
$("#inp").click(function() {
var testD = $("#testD");
testD.append('<br>' + $('#in').val());
localStorage.setItem('testD', testD.html());
});
});
</script>
</body>
</html>