Так сделано на сайте что вы предоставили
<div class="col-lg-8">
<img id="playimage" class="img-responsive" src="assets/img/screen-login-play.png" alt="Using our step-by-step program your school can set up a parent teacher conference in just a few minutes.">
<div id="videoDiv" class="col-lg-12" style="display:none">
<iframe id="player1" src="https://www.youtube.com/embed/uWlLvYknOcE?enablejsapi=1&theme=light&showinfo=0" width="630" height="354" frameborder="0" webkitallowfullscreen="true" mozallowfullscreen="true" allowfullscreen="true"></iframe>
</div>
</div>
При клике
function() {
$('#player1').width($('img#playimage').width());
$('#player1').height($('img#playimage').height());
$('#videoDiv').show();
$('#playimage').hide();
player1.playVideo();
}