Usually preceded by some form of the verb "to have", it is an English idiom meaning "not to know."
To say "I have no idea" simply means "I don't know." However, it is slightly more emphatic than "I don't know", i.e., more like "I really don't know." A similar, equally idiomatic expression is "I don't have a clue."
Often used in the second person followed by an exclamation point: "You don't have an idea!" In this case it typically implies there is more to something than appears immediately obvious. A similar expression is "You don't know half of it!"
When used in the past tense, it is often a form of apology. For example, if one says something that offends a person or a group of persons (which is very easy to do for us who are not native English speakers and do not know all the subtle idioms of the English tongue), and eventually realizes it was offensive, one might apologize by saying: "I had no idea." In that case, one is often expected to blush.