The term 'visibility' is used in the context of search engine visibility. When a website is not indexed(or just few non-useful pages are indexed), the site is said to be invisible to the search engines.
The causes of such invisibility could be with search engine optimization(SEO). An webpage author, at his wish, can also make the webpages invisible by using the META NOINDEX tag.
Search engines that claim to find invisible website are the ones with better(?) crawling. They may also not respect the META NOINDEX tag and index a page against the wish of the author.