The Works Progress Administration created SOUNDEX in the late 1930's to help the searching and storing of surnames that are pronounced the same but are spelled differently. Soundex is a way of assigning sound codes to names. Interestingly, the US government indexed surnames based on SOUNDEX when collecting results of census records.
Census example below
select SOUNDEX('Smith')
select SOUNDEX('Smyth')
select SOUNDEX('Smithe')
select SOUNDEX('Smythe')
All Return S530
Other real world use cases
Misspelled words:
select SOUNDEX('Chicken')
select SOUNDEX('Chikin')
Both return C500
Other real world use cases
Some states use SOUNDEX to generate license plate numbers
http://www.highprogrammer.com/alan/numbers/dl_us_shared.html