Someone with numbness has no feeling in some part of her body. You might, for example, experience numbness in your foot after sitting with it tucked under your leg for an hour.
The noun numbness is good for describing what happens when you lose physical sensation, either temporarily or permanently. Numbness can be a symptom of various illnesses and conditions, but it can also be the result of sitting in an awkward position. You can also use the word to talk about an emotional lack of feeling. The death of your dog might make you experience a kind of numbness, losing your interest in the world around you.