When you block someone on social media, you prevent them from seeing your posts on that social network. Blocked users also can't follow you, send you messages, or tag you in photos. You can't add blocked Twitter users to lists. Blocked users can still @mention you in a post, but this won't count against your engagement metrics.
However, keep in mind that it's also pretty easy for blocked users to see content you've posted publicly. Use the privacy settings on each social network to better control who sees your posts.