Google has expanded its search history feature to include web history too. Simply, this means that while previously it recorded only your search history, now it includes the whole of your online activities, which includes searches, videos, images and new stories. According to Web History Help Center:
With Web History, you can view and search across web pages you’ve visited in the past, including Google searches. Web History also provides interesting trends on your web activity, such as which sites you visit most frequently and what your top searches are. Finally, Web History helps deliver more personalized search results based on what you’ve searched for and which sites you’ve visited.
You can remove items from your search history. But is that a permanent deletion or just that you can’t see it anymore? I am not sure. Danny Sullivan has an extensive review of at Search Engine Land.