Adam G. Carstensen wrote an article, An Introduction to Double Metaphone and the Principles Behind Soundex for the “Business Intelligence Network”, that explains the background and history of Soundex:
Immigrants to the United States had a native language that was not based on Roman characters. To write their names, the names of their relatives, or the cities they arrived from, the immigrants had to make their best guess of how to express their symbolic language in English.
The United States government realized the need to be able to categorize the names of private citizens in a manner that allowed for multiple spellings of the same name (e.g. Smith and Smythe) to be grouped. Thus, the United States Census bureau, more specifically Robert C. Russell of Pittsburgh, Pennsylvania created an algorithm capable of indexing the English language in a way that multiple spellings of the same name could be found with only a cursory glance. Thus, in 1918 Soundex was born.
Even though many genealogy programs and genealogy websites can handle Soundex for you, it’s still interesting to read about how and where it came from.