A Backlink Analysis helps to identify a website's pros and cons. In addition, it should include an audit of competitors to understand where the site stand. Then a brainstorm can be done on link targets and content production. Finally work can be prioritised depending on potential and complexity, setting targets: quantity and quality links for the next quarters with a focus on > brand building.
Like it has been the case since over 20 years, backlinks are key to SEO success and still define the reputation and popularity of your brand on the web. However, backlinks do not work like 20 years ago, and far from it. It is now much more about quality of the links and relevancy. It is crucial to understand where you stand, plan, execute and control your backlink activities.
Getting many backlinks from any website, paying links off from unrelated websites, or websites operating from a different country or with a different language are some example of wasted efforts. Most importantly, if the website which is linking to you has a poor reputation itself its value will be only minimum; worse if it is considered a spammy website, the link might even lower your website's reputation.
Getting a link from a reputable and relevant (to your industry) website is a great achievement. However keep in mind the actual page the link is appearing on is the real deal. If the page itself has little exposure, little number of internal links and/or traffic, its impact will not be as positive as if it was on the homepage for example. On the contrary, if it appears in every page of the site, this might seen as spammy backlinking so avoid that extreme as well.
It is very important and useful to look at your successful competitors to analyse: how they get their (high quality) links, the domain authority and quality of their backlink profile, ratio follow/ nofollow, anchor text, ratio quality links, number & quality of referring domains
Link Explorer is a tool from Moz, previously known as Open Site Explorer. It is one of the main tools used in SEO to perform an Backlink Audit. Results vary from tool to tool although there majority of links found by each of the main tools (ahrefs, SEO Majestic, SEMRush to name a few).
Anchor text need to be as natural as possible, avoiding click here or other misleading text. Very often the brand name is the most used anchor text. Make sure the ratio of nofollow links is not too high. nofollow means that the website linking does not want to commit the link as sign a trust and therefore pass link juice (authority). It is totally acceptable to have a certain percentage of nofollow links but if this ration gets to high, this is sign that your website is not trusted.
.gov and .edu sites have by essence a lot more trust and power as .com for instance. If you have the opportunity to get a link from such sites and it makes sense to your business - bringing in at the same time quality & relevant traffic - this link will very likely be beneficial.