A referring domain is the domain where your backlinks / inbound links are coming from.
A backlink is the individual link from a referring domain.
For example. We have 10 backlinks from Wikipedia across different wiki pages,. In SEO terms that would count as 1 (one) referring domain, and 10 (ten) backlinks.
From an SEO perspective generally increasing referring domains is more important that increasing the number of backlinks from a single domain.