"I'm not sure whether I spelled this name right"
Checking this box maps the word you entered into a four character string, which captures some of the phonological properties of the search word you've entered (see the NARA Soundex Coding web page). This string is then compared it to the "soundex" strings of all names in this database. The matches will be included in your search results.
The soundex algorithm was developed in the beginning of the last century. Better algorithms have since been developed, so don't expect wonders. But maybe it will help you to find what you're looking for.