Edit in JSFiddle

var op = $("#output");
// if you just do this then any new p tags added wont have the click event 
//$("p").click(function() {
//    op.append("p clicked <br/>");
//});

// with on even the newer ones will also have the click event
$("body").on("click", "p", function(e) {
    op.append("p clicked <br/>");
});

$("#btn1").click(function() {
    $("#div1").append("<p>something</p>");
});

<div id="div1">
    <p id="p1">some paragraph 1</p>
    <p id="p2">some paragraph 2</p>
</div> <br/><br/>
<input type="button" id="btn1" value="Add"/>
<br/><br/>
<div id="output"></div>

#btn1{margin:2px; padding:10px}
p{margin:5px; padding:5px; border:red 1px solid;}