jQuery .append() can be used to add text to an div. The text can contains tags inside it.
<script src="//ajax.googleapis.com/ajax/libs/jquery/2.1.4/jquery.min.js"></script>
<div style="background-color:lightblue;" id="msg">First line<br></div>
<button onclick="addText()">click to add text</button>
<script type="text/javascript">
function addText() {
$("#msg").append("Added text<br>");
}
</script>