Instinctive shooting is simply using your instincts to guide the arrow where you want it to hit. The theory behind this technique is that using your hand eye coordination, with your hands guiding the bow and your eyes doing the aiming you will be able to accurately hit where you are looking. Some shooters will argue that there is no such thing as shooting purely instinctive. Their argument is that seeing the arrow is necessary even if your only using your peripherals for some reference. I would probably fall somewhere in between these two arguments. I will often focus as much as possible on the spot I want to hit, as well as use my peripheral vision for a reference on the arrow.
The process of aiming instinctively recquires the archer to have good shooting form. There are several videos that are excellent for learning proper form, these include Instinctive shooting with Paul Brunner, and the masters of the barebow collection. Once proper form is achieved the aiming process is very simple. It all boils down to concentrating as much as humanly possible on the spot that you want your arrow to hit. This technique like any other takes many sessions of practice to master, but it is well worth it when shooting a traditional bow!