SEO visibility is commonly understood as "how much a website shows up in Google search results". Different platforms have different ways of estimating how well a website competes in the SERPs compared to its competitors.
What SEO visibility metrics does Ahrefs have?
At Ahrefs, we use the following metrics to gauge visibility:
Impressions, which sums up the search volume for all the keywords that the target website ranks top 10 in. You can check any website's impressions in Site Explorer.
Share of Voice (in Rank Tracker), which is the percentage of clicks your website receives, versus all the clicks that all results in the SERP receive, for all keywords it ranks for:
Even if a website is not receiving traffic from google, it could still be showing up in Google results. For both metrics: the higher it is, the better your website's visibility would generally be. You can use these metrics to see how well your website stands against its' competitors.