It's all kind of metaphorical. On the mountain, they learned how to earthbend from the Badger Moles. So they created that secret tunnel so they could continue to be in love, without their two villages knowing. In the end, the man died in one of the wars. The woman was so enraged, she nearly destroyed both villages with her powerful earthbending. In the end, she spared them and said the war was over. In their honor, the city of Omashu was established.