Samsung is know to do some innovative things whit their yearly flagship phone. With the Samsung Galaxy S6 edge, they brought a dual edge display to the table. It doesnt have too much functionality, but the design makes it the best looking phone to date, in my books. It is gorgeous! Very comfortable to hold in the hand and very accessible form factor. However, as there is more glass, it is that much more fragile so you need to be a little more careful. The edge lets you access contacts and frequently used apps which makes it a good multitasking phone. The edges light up in specific colours to inform you who is calling, which is pretty handy. But that is about it. Rest of the phone is entirely the Galaxy S6.
Do I think its worth the extra money over the Galaxy s6 standard? Yes! It is infinitely better looking, and has 2-3 extra features. Totally worth it