You can use a lightbox.

It's really simple to use. Include the script tags and CSS stylesheets in your HTML file, and then simply use:

<a class="example-image-link" href="images/image-1.jpg" data-lightbox="example-1"><img class="example-image" src="images/thumb-1.jpg" alt="Girl looking out people on beach"></a>

I've taken Scott Marcus' answer and adapted to click, which was your original request.

The main diffence is the addition of a tags targeting elements on the page and using :target in the css.

img { 
  width:200px;
  border:1px solid black; /* This is only added for testing purposes*/
}

.thumbnail:target {
   width: 500px;
   height:auto;
   position:relative;
   /* push image to the right by 1/2 the screen width and 1/2 the image width */
   margin-left:calc(50% - 250px);
}

<section id="main">
  <div class="inner">
    <div class="box alt">
      <div class="row 50% uniform">
         <div class="4u">
           <figure>
             <a href="#image1">
             <img src="https://pbs.twimg.com/profile_images/562466745340817408/_nIu8KHX.jpeg" alt="" class="thumbnail" id="image1">
             </a>
             <figcaption>Marble</figcaption>
           </figure>
         </div>

         <div class="4u">
           <figure>
             <a href="#image2">
             <img src="http://www.critterbabies.com/wp-content/gallery/kittens/cats-animals-kittens-background-us.jpg" alt="" class="thumbnail" id="image2">
             </a>
             <figcaption>Marble</figcaption>
           </figure>
         </div>
         
         <div class="4u">
           <figure>
             <a href="#image3">
             <img src="http://www.warrenphotographic.co.uk/photography/bigs/08482-Fluffy-ginger-female-kitten.jpg" alt="" class="thumbnail" id="image3">
             </a>
             <figcaption>Marble</figcaption>
           </figure>
         </div>
         
       </div>
     </div>
   </div>
 </section>

I've taken Scott Marcus' answer and adapted to click, which was your original request.

The main diffence is the addition of a tags targeting elements on the page and using :target in the css.

img { 
  width:200px;
  border:1px solid black; /* This is only added for testing purposes*/
}

.thumbnail:target {
   width: 500px;
   height:auto;
   position:relative;
   /* push image to the right by 1/2 the screen width and 1/2 the image width */
   margin-left:calc(50% - 250px);
}

<section id="main">
  <div class="inner">
    <div class="box alt">
      <div class="row 50% uniform">
         <div class="4u">
           <figure>
             <a href="#image1">
             <img src="https://pbs.twimg.com/profile_images/562466745340817408/_nIu8KHX.jpeg" alt="" class="thumbnail" id="image1">
             </a>
             <figcaption>Marble</figcaption>
           </figure>
         </div>

         <div class="4u">
           <figure>
             <a href="#image2">
             <img src="http://www.critterbabies.com/wp-content/gallery/kittens/cats-animals-kittens-background-us.jpg" alt="" class="thumbnail" id="image2">
             </a>
             <figcaption>Marble</figcaption>
           </figure>
         </div>
         
         <div class="4u">
           <figure>
             <a href="#image3">
             <img src="http://www.warrenphotographic.co.uk/photography/bigs/08482-Fluffy-ginger-female-kitten.jpg" alt="" class="thumbnail" id="image3">
             </a>
             <figcaption>Marble</figcaption>
           </figure>
         </div>
         
       </div>
     </div>
   </div>
 </section>

Without seeing your CSS code for .show, I can't really determine what went wrong, but adding some CSS code for .show and .popuptext, everything works!

EDIT: I have also added a simple animation code to animate a "popup"

.show {
  display: block!important;
  /* The bottom is for animation when the popup gets shown */
  animation: popup .2s 1;
}

@keyframes popup {
  from { transform: scale(0); }
  to { transform: scale(1); }
}


.popuptext {
  display: none;
}

<nav>
  Navigation Bar
  <ul>
    <li>
      <div class="popup" onclick="myFunction()">
        Myself
        <span class="popuptext" id="myPopup">My description</span>
        <img src="/images/picture.jpg" alt="My picture" />
      </div>

      <script>
        function myFunction() {
          var popup = document.getElementById("myPopup");
          popup.classList.toggle("show");
        }
      </script>
    </li>
    <li>Contact</li>
    <li>Other</li>
  </ul>
</nav>