Previously, your web history (Google searches and sites visited) has been separated from other Google products because it can reveal sensitive info like location, age, sexual orientation, marital status, and more, but after the changes take effect, your web history will be used to help make your Google experience more relevant. If you'd rather not have your web search history combined with information gathered from other products like Google+, YouTube, and so on, you'll want to delete your web history posthaste. Take note that this is different than just clearing your browser's history and cache — if you're signed into any Google product (Search, Gmail, Google+, etc.), Google will track your search data within its database.
Find out how to clear your Google search history with the step-by-step instructions in the gallery, and since we're talking about privacy, you should also read up what the new Online Consumer Bill of Rights means for you.