It seems this is less about explaining the beauty of the art, but rather about explaining the importance of the art to you. Frankly, I just tell my loved ones that it helps me with my ADD (I don't have ADD). They don't understand jiu jitsu but they're glad I found something keeping me around the shady local boxing circles..
I don't even think there's a way to explain how beautiful jiu jitsu is to a candid listener. To me, in order to "get" it, you have to sign up for training. Roll around with people around your own level for a month or two. Once you start hitting some moves on dudes and think you know jiu jitsu, roll with higher level guy. Even with a high level white belt, you'll be humbled. I think at that moment is when a person "gets" jiu jitsu.. When even with all your efforts put towards executing the same techniques the other guy is doing is not enough and you're tapping out every few seconds. How many people will go through all that just to understand a certain art? Not many that I know..I'm just thankful that I did