When one desensitises a horse, human or any other living being to a stimulus the stimulus is applied up to the point where the stimulus is not even registered in the mind of the being. A ticking clock in you grand parents house is a good example. When you visit them it drives you nuts, but they don't even hear it. After a day or so neither do you. Go home for a while and the re-visit them and its' back to driving you nuts again, desensitisation in not a persistent phenomenon.
In the horse world let us say that you play with a plastic bag around your horse for hours. To start the horse in scared, but slowly it comes to accept the bag. If you are desensitising the horse you then continue to the point that the horse does not even know that the bag is there anymore.
This has evolutionary benefit as a phenomenon. There are certain stimuli which are continuously in the sensory range of a horse, the sun or wind for example. It is a waste of energy to respond to these stimuli and could distract from important stimuli like a predator. Therefore there is a mechanism in the brain to totally ignore common stimuli which we tap into when we desensitise a horse.
Unfortunately folks tend to desensitise horses to intermittent stimuli like plastic bags. They keep them in the horses sensory range until the horse does not respond anymore. This has gone past the learning stage about the bag and into the totally not noticed stage. The bag ceases to exist as far as the mind is concerned. The snag is that if in the distant future a bag reappears then for the horse it is a new stimulus and they react accordingly.
James was a strong advocate of making a horse confident with a stimulus, not desensitised to it. Thus the stimulus should only be applied to the point that they are confident and curious about it, not totally ignoring it. This form of learning is much more persistent and thus the bag is less likely to provoke a strong response in the future. It does take some skill at reading the horse to know precisely when to quit however and I for one committed the sin of desensitising Filly to many stimuli by not spotting the signs early enough and quitting at the confident stage.