tactile - Dictionary definition and meaning for word tactile
CON-tact - If you are in contact with something, you are in touch with it and hence it is tactile.
It sounds similar to Reptile(class of animals e.g Snake).Now this animals e.g snake are quite sensitive or react suddenly when see something .thus quite sensitive and as we can't touch them so related to touch.
tactile sounds like textile, we are in constant touch of clothes, it implies the meaning
come in-tact means come in touch. So, tact means: sense of touch.