It means someone has clicked that button, and shared the link/banner of your comic on one of their social media accounts - Twitter and/or Facebook seems the most common place. : ) It's a way for them to tell their friends that "Hey, look at this cool thing I'm reading!" while linking back to your comic, and it's a GREAT way to get more attention for your comic.
I rarely use the share-button myself, but instead link manually to comics on Twitter, but it's the same principle.
