Link Pruning is what webmasters and SEO people do to find and remove bad backlinks to a website. A website can be penalized in the rankings by Google for having what look like paid links or for being part of what looks like a linking scheme (reciprocal or round-robin linking), or just really dodgy websites. If one can't get them removed, then one adds the links to the "disavow" list and submits that to Google. A black hat SEO technique is to purchase links from dodgy sites to your competitors, so as to drag them down in the rankings. If that technique has been applied by one's competitors to one's own website, it is discovered and handled with a link pruning evolution.
In our SEO shop, link pruning also includes looking through our website's outbound links to make sure that our outbound links aren't broken, that they don't point to dodgy sites, and that they aren't redirected to other pages. As the months and years fly by, websites experience "link rot" where outbound links go bad. These outbound links can hurt a website's ranking at Google. It's part of keeping a website up-to-date.