When you run a search on any engine, such as Google, you likely assume that no one else really takes the time to look at it. It's stored in your search history on your device, but you don't think any outside parties are going to look at it or connect it with you specifically. And, in the vast majority of cases, this is certainly true.
However, this data is stored by the search engine. They know who ran the search, what terms were used and things of this nature. Recently, it has come to light that the U.S. government has executed keyword warrants as a way to gather information on potential suspects.