Google, the world's most popular search engine, is asked to remove a huge amount of URLs from their search results each year for a number of different reasons, and by a number of different entities, which means the fact that the number of removed URLs has jumped over 2 billion should not be all that surprising. Another aspect that is unlikely to be too surprising is the fact that the number one reason for removal requests is still piracy of digital content. The 2.13 billion odd takedown requests that Google has honored across roughly 1 million websites represents just over 90% of the total requests that they have received.
Google has been keeping track of requests and actual delistings since July of 2012, and have put together a graph, included below, that shows the trend in requests over the years. In the nearly five years that requests have been tracked, they have gone up slowly, until a bit of a spike lasting from about the middle of 2015 until just recently. This is reportedly indicative of an upward trend in online piracy of various sorts; given the sheer number of ways to watch, listen to, read, and play pirated content these days (as well as how much cheaper and easier it now is to find ways), that guess may not be too far off the mark. Although, what is also likely to be a big contributor to the spike is an increase in the use of algorithmic finding and reporting of piracy sources.
Interestingly enough, requests for takedown sometimes end up coming from or being aimed at strange places, sometimes both at once. The United States Government, for instance, has sought to have Google delist some of the content on its own websites, such as the White House website. Some governments seemingly attempt to use Google's request system for outright censorship. Sites that tend to index or reference copyrighted works or their names are, of course, common targets of requests, as are sites like Facebook that host personal data that somebody may end up regretting putting out there. Often, these requests end up being honored under the "right to be forgotten" or similar laws.