In the CodePen Editor View, the preview pane is essentially a browser window (it's an
<iframe> of your code). It does just about everything a normal browser window does, including opening links in the same window. Unless—it's told to do otherwise.
So, if you put a link to CodePen inside your Pen, you can end up with CodePen-ception — CodePen-in-a-Pen (hat tip to John Chin-Jew, who coined the term).
— John Chin-Jew (@johnchinjew) October 3, 2015
One workaround is to add
target="_blank" to your links, like this:
<a href="http://www.codepen.io/you/pen/SLUG" target="_blank"></a>
That will make your links open in a new window/tab.
Or, you can work with it to make something cool! NobodyRocks took the CodePen rabbit-hole to a new level with this Phone styled iframe.