You use have got to say that someone has a particular thing, or to mention a quality or characteristic that someone or something has. In informal American English, people sometimes just use 'got'.
You use have got to when you are saying that something is necessary or must happen in the way stated. In informal American English, the 'have' is sometimes omitted.
People sometimes use have got to in order to emphasize that they are certain that something is true, because of the facts or circumstances involved. In informal American English, the 'have' is sometimes omitted.