First thing's first Wolfram|Alpha is not your conventional search engine but is a computational engine that provides you with answers related to probably anything that has numbers or digits attached to it. It computes the answers by utilizing the structured database on the fly.
What can one do with Wolfram|Alpha ?
With Wolfram|Alpha you can get answers to your queries that may have numbers attached to it. It can answer questions related to mathematics, economics, weather, physics, constants, currency exchange and much more topics. It also provides a user with various visualizations(charts, bars, graphs) etc along with the results.
Following are some of the usage scenario's for Wolfram|Alpha:-
1. Mathematics :-
a) example query : integrate x2*sinx
now as can be seen from this figure, it provides you with all the information you need along with the graphs of the integral function.
b) example query: 10^5 mod 35
would produce output's containing the result 5 , alternative representations etc.
these are just few of the examples, you can try your own at Wolfram|Alpha .
2) Economics :
example query: compound interest for 10000 at 5% for 3 years
b) example query: GDP growth of countries
3) Constants: The thing that i like the most about it is that it can compute the value of constants to as higher precision as one may want to. You just have to click on the more digits button and it will calculate the values to a much higher precision.
For ex: pi
4) Weather and general information:
Wolfram alpha can calculate where you are by using your ip address and then provide you the relevant information.
For example:
let's say you type "weather" then it will provide you with the weather information for your city automatically by looking at your ip address. Just take a look at the following output.
These are just few of the many possible things one can do with wolfram alpha.
Shortcomings:-
the only thing that Wolfram|Alpha lacks is that it provides old data for certain queries like "gdp growth india" in this case it provides the 2005 estimate.
The fresh data acquisition is the only thing that one would want Wolfram|Alpha to work upon.
