Our skin has many types of neurons that allow us to feel upon touch. They are receptors of different kinds that are triggered by different stimuli but activate the same way upon triggering. Thermoreceptors trigger on change in temperature. Nociceptors trigger on pain. Mechanoreceptors trigger on mechanical stress. These receptors send signals to the spinal cord and the brain to register a touch.
A combination of these receptors spread across an area leads to a triggering in various nature depending on the stimuli. This is how we are able to distinguish textures and types of touch.
In general, robots are really good at predictable motions that can be broken down to a set of axis and have a known distribution of forces. This is why a robot is used for welding different parts of a vehicle body but a human operator is used to install an intricate wiring harness.
Tactile feedback would be a large improvement in the feedback loop for robots if they need even a fighting chance to learn more complex tasks. A new technology developed by aat the University of Hong Kong allows robots to detect tactile inputs at a super-resolution.
The system uses a flexible magnetized film as the skin and a printed circuit board for the structure. The film creates a magnetic field within the device and the subtle changes in the field is sensed to determine the touch.