The quantity of AP courses is important; USNA looks for rigorous academics. My DS took a lot of APs in high school - 1 as a sophomore (actually counted as 2 since it was AP Biology + lab), 3 as a junior, and 6 as a senior. As part of the online application, you are asked to list the courses you will be taking your senior year, and that is how they will know what you have taken (until they receive your high school transcript). USNA will not know the results of your senior AP tests until long after you have been accepted, and most likely won't get them until after Plebe Summer starts. My son's arrived about two weeks after I-Day.
The value of a high score on the AP exams comes into play during Plebe Summer when you have the potential to validate (be exempt from) certain courses. A 4 or 5 on an AP exam might mean you do not have to take the entry-level course that others are required to take. There is a page on the USNA website that tells you what your AP score needs to be in a particular subject in order to validate a class. However, you also have to take a validation test during Plebe Summer in order to validate certain classes. They want to make sure that you still know the material!