The NYSIIS algorithm is a phonetic code algorithm used to index words that are pronounced similarly. It is sometimes used to match an approximate pronunciation to an exact spelling (somewhat similar to spell checker).
For example, you are looking for someone's information in a database of people. You think that the person's name sounds like "John Smith", but it is in fact spelled "Jon Smyth". If you did a simple search, looking for an exact match for "John Smith" you would not get any results. Instead, you can index the database using the NYSIIS algorithm, then when you go to search use the NYSIIS algorithm again on the input. Both "John Smith" and "Jon Smyth" are indexed as "JAN SNATH" by the algorithm, giving you the correct match.