Stay connected to your board
You don't want to spend time chasing your SUP around. What you really want to do is to spend as much time up on the board as possible. Therefore the surf leash / SUP leash is a crucial part of your set up. Without a leash, even in a light breeze or small waves of current, your board will drift out of your reach in a matter of seconds. If you are way out on the ocean, this can actually be quite dangerous, and a leash simply prevents the drifting from happening.
So when you rush out to buy your SUP leash, there are a few things to consider. One of the things to consider is whether you want a coiled or a straight leash. The advantage of a coiled SUP leash is primarily that it keeps out of the water. That is why it's often chosen by race SUP's since it minimises any drag from the water surface. A straight leash is more traditional but almost only used by SUP surfers riding waves.
Where to attach the SUP leash?
The place, that the SUP leash is attached to the surfer varies, but the typical points are the calf and the ankle. The calf is often favored by surfers that like to move a lot on the board while they ride the waves.