What is the meaning of mme in french?

Mme is the abbreviated form of "madame", i.e. Mrs.

Melle / Melles. ("mademoiselle/mesdemoiselles) is the translation of Miss/Misses

Ms. has no French equivalent - French people tend to use Mme when the marital status is irrelevant to the purpose of the letter. In spoken French we use "madame" or "mademoiselle" depending of the context: an older person will be called "madame", whereas a younger one may be called "mademoiselle"