If you see something you want on a Lightning Deal and you can add it to your cart, you have 15 minutes from that moment to complete your purchase. If you get on the Waitlist, you have to stay on Amazon.com and watch for a window to pop up and offer you the deal and accept it within a minute, then complete the purchase within 15 minutes. If you're on the Waitlist, you may get the deal if someone else does not complete their purchase in the allotted time, or if they change their mind and delete from their cart. When you add to the Waitlist, it'll tell you what number you are and what your chances are of getting the deal.
Hope this helps!