Most of it is that Steve Jobs has created the computing world we have today and has driven the market and design for decades. Sure, he isn't everything, he didn't invent everything, he didn't do it all, he doesn't have complete control, but Steve Jobs has been the genius of home computing for the average person since he entered the field in the mid-70s.
So he has the vision because he opened a market, expanded it again and again, made semi-useful tech into universally craved tech, and his vision steers the market more than any other single person has done since computers were developed.
The best thing he does to connect to people is that he tries to connect to people. You think Steve Ballmer or Gates or any other major computer person connects with people? NO. They parade about like tyrants--I am here and I AM THE GUY. Steve has repeatedly come on stage to say, "This is what I have made FOR YOU. This is a new device I developed to DELIGHT YOU, entertain YOU, be easy for YOU to use. This device helps YOU. Please take a look at what we've done FOR YOU."
It's a no duh. Jobs does something few others do in the computer world, and it drives his entire philosophy. The guy gets excited when he creates stuff FOR YOU.