Boy K, is a mysterious young boy that, initially, only appears to Aoto.
Thus making Aoto believe he is an illusion made up by his mind. In reality, he is actually the key to the Divine Gate that has been watching over Aoto. He only reveals himself to those that have experienced 'true despair'.
Besides Aoto and otherworldly beings (i.e. gods/wizards), Undine has seen Boy K anytime he spoke to Aoto. Later in the story, Midori and Akane were able to see him after losing their loved ones.
Within the anime,
Boy K was like a guide who watched over Aoto. His goal was to guide Aoto to the Divine Gate. Throughout the series we see that Boy K constantly gives commentary about Aoto's life to him. Through his commentary, he forced Aoto to face his inner thoughts and demons. He knew that Aoto would never consciously reveal his weakness, to himself or others. Slowly as Aoto started to break down that ice barrier he had placed around his heart, Boy K started to 'push' Aoto to the direction of the gate.
When fighting the gods, he stated that after facing such 'true despair' in their lives, they deserve the chance to control their future. The gods rebutted, stating that this much power could corrupt humans. That their, the gods, goal was to control the peace and just let things move forward. Boy K argued back that gods have just the same chance of becoming corrupted with the power.