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How can I pass some data or call a function on the parent window from a popup window?

The user will click a link which will open a popup on the same website, once he is finished with the popup, I want it to send the new data back to the parent window, or call a function on the parent window.

The window.opener object is what you're looking for, used it from within your popup like so to call the a function of the parent window:

window.opener.yourFunc() 

Here is a fun and easy demo that is heavily inspired by this answer to a similar question (but modified for my own purposes to help investigate the most difficult bug of my career).

Create 2 files (in the same directory) as follows:

parent.html

<button type="button" onclick="popup('popup.html', '', 800, 200);">Add My Card</button>
=&gt;
<span id="retrievedData">No data yet.</span> 
<script>
 function popup(url, title, width, height) 
 var left = (screen.width / 2) - (width / 2);
 var top = (screen.height / 2) - (height / 2);
 var options = ''; 
 options += ',width=' + width;
 options += ',height=' + height;
 options += ',top=' + top;
 options += ',left=' + left; 
 return window.open(url, title, options);
 

 function setData(data) 
 console.log(data);
 var strData = JSON.stringify(data);
 document.getElementById('retrievedData').innerHTML = strData;
 var requestBinUrl = 'http://requestb.in/18u87g81';
 window.location.href = requestBinUrl + '?data=' + strData;
 
</script>

popup.html

<script src="//ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
<form id="popupForm" name="f"> 
 <select id="urlField" name="url">
 <option>
 http://date.jsontest.com/
 </option>
 <option>
 http://time.jsontest.com/
 </option>
 <option>
 http://md5.jsontest.com/?text=HereIsSomeStuff
 </option> 
 </select>
 <div><input type="submit" /></div> 
</form>
<script>
 $('#popupForm').submit(function(e) 
 e.preventDefault();
 var url = $('#urlField').val();
 console.log(url);
 $.ajax(
 url: url
 ).then(function(data) 
 console.log(JSON.stringify(data));
 window.opener.setData(data);
 window.close();
 );
 ); 
</script>