DOUBLE NEGATIVE IN ENGLISH SENTENCE

A double negative occurs when two forms of negation are used in the same sentence. Multiple negation is the more general term referring to the occurrence of more than one negative in a clause.

Languages without negative concord typically have negative polarity items that are used in place of additional negatives when another negating word already occurs. Examples are "ever", "anything" and "anyone" in the sentence: "I haven't ever owed anything to anyone" (cf. "I haven't never owed nothing to no one) in negative-concord dialects of English. Note that negative polarity can be triggered not only by direct negatives such as "not" or "never", but by words such as: "doubt" or "hardly" ("I doubt he has ever owed anything to anyone" or "He has hardly ever owed anything to anyone").

Stylistically, in English, double negatives can sometimes be used for understated affirmation (e.g. "I'm not feeling bad" vs. "I'm feeling good"). The rhetorical term for this is litotes.

In standard written English, when two negatives are used in one sentence, the negatives are understood to cancel one another and produce a weakened affirmative. However, in many dialects, the second negative is employed as an intensifier and should be understood as strengthening the negation rather than removing it.

Two Negatives Resolving to a Positive.

In Standard English, two negatives are understood to resolve to a positive. This rule was observed as early as 1762, when Bishop Robert Lowth wrote A Short Introduction to English Grammar with Critical Notes. For instance, "I do not disagree" could mean "I certainly agree". Further statements may be necessary to resolve which particular meaning was intended.

Because of this ambiguity, double negatives are frequently employed when making back-handed compliments. The phrase "Mr. Jones was not incompetent." will seldom mean "Mr. Jones was very competent" since the speaker would have found a more flattering way to say so. Instead, some kind of problem is implied, though Mr. Jones possesses basic competence at his tasks. 

Source: http://en.wikipedia.org/wiki/Double_negative