Why does blowing on hot soup help to cool it off?

It's because of evaporation. Evaporation cools down a liquid because the most energetic molecules leap off the surface and leave the slower-moving molecules behind. Slower-moving means lower temperature. The more a liquid evaporates, the more it loses heat.

Water Vapor

The hot soup forms a little cloud of vapor above it that prevents more evaporation from taking place.

The fast-moving molecules can't escape the soup any more, because this little fog of water vapor has saturated the air. It just can't take any more vapor, but blow that cloud away and the fastest molecules can escape the soup!

The more you help the fastest molecules to escape the soup, the more you help the soup to cool off.