Heat transfer occurs through surfaces. The hot soup surface is in close contact with the surrounding cooler air and they quickly equilibrate, but further heat transfer is limited by the time it takes for heat from the interior of the soup to diffuse or convect its way out to the (cooler) surface. Stirring the soup overcomes these limits and speeds the heat transfer process.
Similarly, blowing air on the hot soup surface accomplishes the same thing for the air side of the equation.
A parcel of soup near the shallow edge of the bowl has more ways to diffuse heat away than does a parcel of soup in the center of the bowl, so the outermost edge of the soup is always slightly cooler than the center.