CVW stands for Candidate Visitation WE. Well-qualified candidates may be invited to spend a long WE at USNA. As I understand the program (someone correct me if I'm wrong), you show up on Thursday afternoon and spend the night in a room with a plebe. You go to class and other activities on Friday. You stay Friday night and participate in Sat. morning activities with your plebe. You leave around noon Saturday.
The benefit is that you get to see USNA and the life of a plebe (more or less) during ac year. Some candidates are simply offered CVWs w/o asking. Some ask. However, many very-well qualified candidates don't, for various reasons, get CVWs. It's a matter of numbers -- more candidates wanting CVWs than spots. Thus, not getting offered one doesn't mean you're doomed. In all honesty, being offered a CVW is a good thing but does NOT mean you are definitely getting an appointment.
If you're offered a CVW and can at all afford to attend (they're not paid other than for recruited athletes, and that's a different thing), you should do so. It's another opportunity to see what USNA is all about. Declining a DVW will NOT hurt your chances.