Although it’s tempting to think of Wolfram|Alpha as a place to look up facts, that’s only part of the story. The thing that truly sets Wolfram|Alpha apart is that it is able to do sophisticated computations for you, both pure computations involving numbers or formulas you enter, and computations applied automatically to data called up from its repositories.
Why does computation matter? Because computation is what turns generic information into specific answers.
To give an amusing example, every school child has at one time or another written a report on the moon, and they probably included the wrong figure for how far the moon is from the earth. Why wrong? Because the distance from the earth to the moon is not constant: it changes by as much as a mile a minute. If you ask Wolfram|Alpha the distance to the moon, it tells you not only the conventionally quoted average distance, but also the actual distance right now, which can at times be well over ten thousand miles off the average. The actual distance is a figure that can be arrived at only by computation based on the moon’s known orbital parameters. It’s rocket science, if you will.