You've likely, at some point, seen a caveat at the bottom of your Google results that some links were removed in compliance with the Digital Millenium Copyright Act. Most of those links lead to pirated content. Year on year, the war on piracy gets more intense as those providing content and those downloading it get smarter, craftier and more ruthless as authorities and copyright holders do the same. Naturally, tons and tons of pirated content winds up being accessible through Google. By no means does this mean that Google condones piracy; the nature of their service simply means links get archived regardless of content. For a huge number of people, Google's search page is their main window to the internet. Thus, year on year, requests to remove pirated content from Google's searches number higher and higher.
Unless somebody is willing to devote a bit of time and energy to a search for pirated content, removal from Google generally means it won't reach them. This archetype fits a large part of the populace that engages in piracy. Between all these facts, it should come as no surprise that Google received 12.1 million link removal requests in the first week of 2016. It should also come as no surprise that, per popular Bittorrent website Torrentfreak, whose site is often used for piracy, an overwhelming majority of those requests are from copyright holders in the music and movie industry. The number of requests during this period each year jumps significantly, almost exponentially, year on year. In the first week of 2012, 274,000 links went missing. Last year, 7.8 million links met their fate in the first week of the year.
When a request to remove a link is entered, it generally takes six hours to get around to reviewing and, if applicable, granting the request. Some requests slip through the cracks, but Google is able to review approximately 90 percent of them, according to an analysis by Vocativ. After a link is taken down, the one who posted the link is notified and can appeal the removal. Naturally, since most services used for piracy are either Bittorrent sharing sites, file storage sites or even Google's own Drive service, they don't actually condone piracy. Since policing their sites would take incredible manpower, they opt instead to simply allow the copyright holders to yank the content from Google and honor any DMCA takedown requests they receive.