A married woman's maiden name is the surname she had until she married. Some married women retain their maiden names when they marry these days.
neé is sometimes used if the writer considers it important to mention the woman's surname before marriage. When I last wrote to me ex-, I mentioned that I had "recently bumped into Mary Leach (neé Bertram)", because I remembered th
née in French is the past participle for born, so when you see Jane Smith née Jones that means she was born Jane Jones and then changed her name to Jane Smith. Her maiden name is Jane Jones, since maiden name refers to the name she was given as a girl child.
Adding to what fivejedjon wrote ... the word neé_ is equivalent to the phrase "whose maiden name was." In most cases the word _formerly_ or _born would also work in place of _neé_.