How significant is CAP? It's as significant as you WANT it to be. Just having an entry on your application that says you were in CAP, isn't significant by itself. Same with asking if JrROTC, Scouts, Band, Sports, Clubs, etc. are significant on your application.
Many people have on their application that they played sports, were in JrROTC, etc. And basically, it showed that they simply "Participated". If you want CAP, or BAND, or SPORTS, or CLUBS, or JrROTC, or ANYTHING to be SIGNIFICANT on your application, then you need to show that you did MORE than JUST PARTICIPATED. EVERYTHING comes BACK to LEADERSHIP!!!
Were you a "Team Captain"? Did you get the Billy Mitchell Award in CAP? Were you a COMMANDER in JrROTC? Were you a section leader, drum major, or other positions of advancement in BAND? Did you make Life or Eagle Scout in Scouts? There are 50+ players on a football team. Not ALL of them are equal. There are approximately 33,000 Senior Members in CAP; Not ALL of them are equal.
CAP, as well as MANY OTHER activities CAN be very SIGNIFICANT on your academy application. But that all depends on what you did in that activity. If all you did was PARTICIPATE, then it will mean very little. You would have been better of being involved in a different activity that you are PASSIONATE ABOUT, and therefor were MORE INVOLVED. As a leader, as a team member, as a mentor to younger members, someone who made an IMPACT to the activity.
CAP is a very good activity. So is JrROTC, Scouts, Band, Theater, Sports, volunteering, school officers, high school clubs, etc. But what's important, is that you are involved in activities that you are passionate about, excel in it, succeed as a leader in it, and make a difference. It's easy to see the difference between someone who is passionate and someone who simply participates.
DON'T TRY AND LOOK FOR SQUARES TO FILL IN ON YOUR APPLICATION. THEY DON'T EXIST!!!
Admissions, ALOs, MOCs, etc. have been doing this a while. They know the difference.
Best of luck.