Why would you choose Alfred over Spotlight?
Solution 1:
One thing is speed. I believe Alfred is currently faster than Spotlight. And, this is specifically for Lion I believe, Alfred learns where Spotlight doesn't.
If I want to launch Adobe Photoshop and start to type 'Ph' Alfred will offer Photoshop as an option and move it to the top with the more I select it.
With Spotlight, Photo Booth with be the first choice, and it will not learn what I want with repeated use. I believe at one point it did, but lost the ability in Lion.
Solution 2:
You already have several answers on the web, like here or there.
I personally use Alfred (+ optional powerpack) for a long time now and cannot live without it. It's (very) fast. I use it to obviously (and efficiently as drummin explained) launch applications, but also do simple calculations, search for files (and then take actions on thoses files, copy, email, open, ...), get definition from dictionary. I also command iTunes, added extensions for currency conversion, .dmg creation, etc...
Can you do all of this with Spotlight? I anyway kept Spotlight on Alt+Space but never used it again ;)
I'm a keyboard guy and do a million things in seconds with Alfred. Clear productivity boost.
PS: a 'spell personnaly' helped me write it correctly in my second sentence, english not being my native language, great help for me... ;)