Our sense of touch is pretty good, particularly in some areas of our body (tongue, fingertips, eyelids). Our tongue has a resolution of 1.1 mm (it can discriminate two points as long as they are separated by at least 1.1 mm) whilst our fingertips have a resolution between 3 and 8mm (our back shoulder resolution, by comparison is 3 to 7cm, ten times less than the fingertips).
It is actually a mix of sensors able to provide information on pressure, temperature, pain and position of the parts of our body relative to one another (and there is a lot of software -brain work- to transform the sensors output into meaning!).
Present artificial sensors tend to be rigid, they lose precision as they are bended, and have relatively low resolution.
This is why this news from the University of Tokyo is so interesting. Researchers have found a way to create very high spacial resolution sensors that can bend in any form.
This is made possibile by using carbon nanotubes, that are extremely small, in the nm range, and graphene. They claim to be so accurate that one of the applications envisaged is to provide doctors gloves with high touch sensitivity that can be translated by software into an image helping a doctor, as an example, to better identify potential cancerous nodules in a breast.
Other applications may be in the area of robots, to provide them with a better sense of touch.
You can get a feeling on the construction of this sensors fabric by looking at the supplementary information provided with their paper (worth seeing).