Google Web History is a feature of Google Search

Google search

Google or Google Web Search is a web search engine owned by Google Inc. Google Search is the most-used search engine on the World Wide Web, receiving several hundred million queries each day through its various services....

 and provided by Google

Google

Google Inc. is an American multinational public corporation invested in Internet search, cloud computing, and advertising technologies. Google hosts and develops a number of Internet-based services and products, and generates profit primarily from advertising through its AdWords program...

, in which all search queries and results that a user clicks on are recorded to. The feature is only available for users logged in to a Google Account

Google Account

A Google Account is a user account that provides access to Google-owned services such as Blogger, YouTube, and Google Groups. A Google Account can be identified either by the username or by their unique permanent ID...

. The feature was renamed from Search History to Web History on April 19, 2007. A user's Web History is used to personalize search results with the help of Google Personalized Search

Google Personalized Search

Google Personalized Search is a feature of Google Search and provided by Google. When a user is logged into a Google Account, all of their searches on Google Search are recorded into Google Web History...

.