When you search a domain, there is an option to view its inbound links (backlinks). This is a curated list of backlinks to the domain that you just searched. You can view more results and, even better, refine them using the link at the bottom of the page. We start with inbound links (to a domain) that are Google-indexed (safe to use) unique (eliminating duplicates from the same domain) and relevant to keywords you want to rank for.
The social icons show how many times that specific piece of content was liked or shared.