Hello Anna,
Great question. The social links that are built into the theme are made to link to your profiles on social networks (for following/liking primarily). If you’re looking to have icons for sharing content socially, you’ll want to add a plugin to do that.
A lot of people like the Floating Social Bar plugin to add those. I personally haven’t used it though. There is an abundance of plugins out there that offer sharing buttons though if you’d like something that’s a bit different. The sharing that’s part of the Jetpack plugin is nice too.
If I can help, just let me know.
Thanks,
Bill