"Wolfram|Alpha aims to bring expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. Our goal is to accept completely free-form input, and to serve as a knowledge engine that generates powerful results and presents them with maximum clarity," explains the "about" page.
Even if the homepage's simplicity reminds you of Google, it's a good idea to check the examples page before entering a query. Alpha can't handle any kind of query, so it's important to know its strengths: advanced Math calculations (graphs, equations, prime numbers computations, matrix operations), conversions, facts about weather, population, food, minerals, people, places.
You can enter simple things like numbers, dates, words, HTML color codes, chemical formulas and you'll get a lot of interesting information. The service shows intuitive visualizations and comparisons to better understand the information.
Wolfram|Alpha could be a great way to expand Google Calculator and other Google OneBoxes.