There are two important backlink quality indicators which work together: relevancy + the authority of the donor website. You can evaluate relevancy just by analyzing the content of the donor website. As for the authority, you can evaluate it with Majestic’s Trust Flow and Citation Flow metrics. These two metrics are important as a pair, because obviously it makes no sense to gain 100 links with low Trust Flow, and only a few links from high authority donor websites won’t drive much traffic to your website.
Another important metric is high-quality in-depth content on a donor page. A high-quality backlink from a good website can be compared to a diamond, because it is really difficult to get. That’s why you should be ready to follow strict requirements. On the other hand, poor backlinks are quite easy to get. However they may hurt your website backlink profile.
With the WebCEO Backlink Checker tool (Backlink Profile) you can evaluate your and your competitor’s backlinks among other important metrics:
link text (or anchor text) which appears on the donor website;
target page is the page of your website where the referring page is linking to;
donor website rating metrics: URL Trust Flow and URL Citation Flow (these are Majestic’s metrics);
link status: see if the link is dofollow, nofollow or toxic;
the number of the donor website’s external links shows the popularity of the donor page; however if the page has too many external links it may be considered spammy.