Dante is a hairless breed of dog known as Xoloitzcuintli, ("Xolo" for short) also known as a Mexican hairless. This breed of dog is one of the oldest breeds in the North America, raised in pre-Columbian times by the Aztecs, Toltec, Zapotec, and also in the areas of Colima.
From Wikipedia: "Long regarded as guardians and protectors, the indigenous peoples believed that the Xolo would safeguard the home from evil spirits as well as intruders. In ancient times the Xolos were often sacrificed and then buried with their owners to act as guide to the soul on its journey to the underworld."
This breed of dog was considered to have supernatural abilities of, being able to see spirits and also to help guide their owners in their journey through the underworlds in death. For the movie, they extrapolated this to have Dante the ability to move back and forth from the physical world to the underworld with ease, acting as Miguel's guardian in both worlds.