There are multiple types of double negatives. Not plus a negative adjective, ain't or won't plus a negative word, and certain words that indicate a negative sentence plus a negative word. The second one was one of the top ten complaints sent in 1986 to the BBC when people were asked to nominate the three points of grammatical usage they disliked. It comes from maths, where minus two minus minus two equals zero. Two minuses cancel each other out.

However, unlike in maths, words have no value, and if you cancel some of them out the entire meaning gets changed. 

We should be happy that usually maths are not compared or used in languages, because it can make things very complex.