According to Medline Plus, the body feature located between the nose and mouth is called the "philtrum." It consists of a groove in the skin and muscle. It can be wide, narrow, short, long, deep or shallow based on genetic background.
The function of the philtrum in most mammals is to aid in sensitivity of the nose by keeping it moist. Dogs offer an example of this, since their philtral grooves sometimes connect to their mouths, sending saliva to the nose through capillary action. Human noses are kept moist by mucus, so human philtra are simply non-functional remnants from an evolutionary ancestor.