Pinning a story means that you choose one story to always feature at the top of your Exposure site regardless of what you publish next. A pinned story (depending on site layout) will also appear more prominent in size and shape.
To pin a story: Simply hover the story you want pinned, click the Pin Story icon and click "Yes, Pin It". You repeat the process to "Unpin" a story. The icon will appear white when a story is pinned.
You can replace a pinned story with any other story.