Damerau-Levenshtein is an edit-distance function which returns the number of edits between two strings. Simplistically, it can tell you how 'different' they are. Levenshtein' will tell you the number of substitutions, deletions and insertions needed to convert one string into the other. 'Damerau Levenshtein' also takes into account transpositions, counting as 1 edit.
The limit argument is a performance hack that allows the functions to return early.
Download the MySQL UDFs or a Java class containing the static functions.