Link pruning is a process of audit of link profile, identifying low quality, unnatural or non-organic links and steps to remove such links. In simple it is just removal of bad links from your website link profile.
What I would say is Link Pruning is a new term in SEO with the effect of latest updates in Google and it would become major part of SEO too.
Link pruning is a identification process of low quality backlinks means spamming links and un relevant website backlinks. I highly recommend remove pruning the low quality backlinks through disavow tool.
Link pruning is process to purify website or blog link structure which means remove unnecessary or spam links from website or blog's backlinks profile. This process will be beneficial to increase regain the lost ranking positions in Google search engine.
Link pruning is the process of removing unnecessary link from website.
After Penguin algorithm update the link pruning became one of the best techniques to purify your website from low-level backlinks.
To prune the website you should:
1. Get the list of website backlinks from Google Webmaster Tools, or Majestic SEO's database
2. Find some good automated backlink research tool and research on backlinks that have low quality
3. Request Webmaster to remove the suspicious back link by sending an email