Here's the explanation directly from the source ( almost )
at min 22:03
Worth watching!
Basically and according to Douglas Merrill former CTO of Google it is like this:
1) You write a ( misspelled ) word in google
2) You don't find what you wanted ( don't click on any results )
3) You realize you misspelled the word so you rewrite the word in the search box.
4) You find what you want ( you click in the first links )
This pattern multiplied millions of times, shows what are the most common misspells and what are the most "common" corrections.
This way Google can almost instantaneously, offer spell correction in every language.
Also this means if overnight everyone start to spell night as "nigth" google would suggest that word instead.
EDIT
@ThomasRutter: Douglas describe it as "statistical machine learning".
They know who correct the query, because they know which query comes from which user ( using cookies )
If the users perform a query, and only 10% of the users click on a result and 90% goes back and type another query ( with the corrected word ) and this time that 90% clicks on a result, then they know they have found a correction.
They can also know if those are "related" queries of two different, because they have information of all the links they show.
Furthermore, they are now including the context into the spell check, so they can even suggest different word depending on the context.
See this demo of google wave ( @ 44m 06s ) that shows how the context is taken into account to automatically correct the spelling.
Here it is explained how that natural language processing works.
And finally here is an awesome demo of what can be done adding automatic machine translation ( @ 1h 12m 47s ) to the mix.
I've added anchors of minute and seconds to the videos to skip directly to the content, if they don't work, try reloading the page or scrolling by hand to the mark.
