Today, Google's search engine has a lot of features that clutter the interface and advanced search features that can't be disabled. The focus has shifted from simplicity to interactivity. Google tries to anticipate your query after typing a few characters, you can filter the results by clicking on an option from the sidebar and you can even preview the results using annotated screenshots.
Until a few years ago, Google tried to find the best search results for your query. Now it helps you find the best query for your search. Google shows search suggestions, automatically corrects typos, ignores words from your query and fetches the list of search results as you type a query. Google search is now a web app that empowers users to adjust the results and to make decisions. It's not a decision search engine, it's just a search engine that lets you decide what are the best results.
Google's results are already personalized using signals like location or search history, but that's no longer enough to sift through billions of search results. The search box can't always capture user intent, so Google had to find ways to extend the search box to the entire search results page.
"As people get more sophisticated at search they are coming to us to solve more complex problems. To stay on top of this, we have spent a lot of time looking at how we can better understand the wide range of information that's on the web and quickly connect people to just the nuggets they need at that moment," explained a Google blog post from 2009 that announced the search options sidebar.
Google is all about reducing the friction of entering a query. You no longer have to "feel lucky" when you type something in the search box because the results are displayed instantly and you can quickly adjust them. Google's results don't have to be perfect because you can customize them until they're perfect for you.
There's one Google doodle that captures the essence of Google's transformation from a simple search engine to an interactive web app. It was used to promote Google Instant, but it's probably the best summary of this post: