a syntactic construction containing two negatives and having a negative meaning, e.g. ‘I didn't hear nothing’ meaning ‘I heard nothing’
The use of not together with another negative word to express a negative idea, as in I don't know nothing, is not standard English. A less glaring error, but still an error, is the use of the second not in It wouldn't surprise me if it didn't rain. There the second not is simply superfluous: It wouldn't surprise me if it rained or, with a different emphasis, It would surprise me if it didn't rain. Double negative forms should only may be used when the intention is to express a positive idea: a not unusual (quite common) request; I can't do nothing (I must do something).not unrelated (there may be a link); not infrequently (quite often); One simply cannot not be impressed (one cannot fail to be). The not un- construction is often used to express a slight reservation in the speaker's mind (Let's say that it was not unimpressive.) and is useful for that purpose. The cannot not construction is usually best replaced by something less ungainly: cannot but be impressed; cannot fail to be impressed. Occasionally more than two negatives in a sequence are encountered: ‘This does not imply that sexual relations that don't risk conception are unrelated to personal responsibility and morality’ — Margaret Drabble