Haptic memory is a type of sensory memory which concerns touch. It's a very short term memory and handles the way we intepret everyday sensations such as pain.
There are two main categories or 'submodalities' within our sense of touch. Put simply, cutaneous sensory input is a feedback from touch on our skin whereas kinesthetic sensory input is feedback from our muscles. If you consider touching an object on your desk, then the feedback of how that feels is likely to be cutaneous. You are sensing the desk, whether it's rough or smooth, hot or cold. If you now push the desk you are likely to start to get a feeling that it's heavy and the feeling starts to arrive via the muscles. You are now experiencing both cutaneous feedback and kinesthetic feedback. And possibly pain !
Note that the actual relationship between haptic, cutaneous and kinesthetic is a little more complex than we describe here. The purpose here is to try and simplify a subject which is incredibly complex.
Haptic perception is the term given to our ability to intepret the sense of touch. It is however possible for haptic sensitivity to be reduced and therefore haptic perception to be reduced. This can happen through injury, burns or other damage to our nerves. There are also a number of diseases that can affect our ability to sense touch. The effect of this can be substantial. Haptic feedback is so natural that it isn't noticed. The lack of haptic sensitivity can prevent walking, restrict the ability to hold objects and so on.
The study of haptic perception has played a major role in the development of robotics. The feedback loop between a robot gripping and object and ultimately knowing how tightly it is being gripped is a crucial factor in developing advanced robots. For example, if a robot is grabbing an object 2cm wide then it can calculate that a grip distance of 1.998 cm will hold that object tightly. But this is very crude and doesn't take into account tolerance or variation on the object itself. If the object is 2.1cm wide then the robot will grip too tightly and if it is 1.9 cm then it won't grip at all. What is required is a feedback loop so that the robot understands the exact pressure being applied to the object so that it reduces it's gripping distance to the point it has grip, but no more.
Due to the nature of the memory test here, we don't currently measure your haptic memory performance. That's not to say that haptic feedback isn't playing a part. If you take this test on a touch screen device such as a mobile phone, then the action of you touching the screen might trigger a small haptic feedback mechanism. Inside your phone there is a small electric motor which vibrates as you touch the screen. This haptic feedback gives you a sensory stimulation that you have touched the screen. Clearly, you may also have an audible 'echoic' stimumli as well if you hear a beep. Therefore, haptics may play a part in the memory test but your haptic memory isn't being directly tested.