There are actually two soft spots on an infant's head and they're called "fontanelles". The posterior fontanelle is a soft spot located on the back of the infant's head. The anterior fontanelle is a soft spot located on top of the infant's head.
An adult soft spot is usually a soft spot found on the side of the skull, instead of the fontanel that are found in an infant's skull. What the adult soft spot does, it actually supports the skull; avoiding a severe head injury.
When first born, it is normal for the top of a puppy's head to be soft. This is called the soft spot or fontanelle and is where the bones of the skull have not yet fused to facilitate the birthing process. Over the next few weeks the soft spot should harden and fuse.