In plain words
What is Guru Pūrṇimā? People take it to be the day on which one offers a little dakṣiṇā to some sannyāsin or great soul and receives initiation into a mantra from him. But that is not the true meaning of Guru Pūrṇimā. Who, after all, is the guru? Because someone gave us a mantra, or someone taught us holy things, we take him as our guru and perform guru pūjā. But this is not the true principle of the guru.
Gurur brahmā gurur viṣṇuḥ gurur devo maheśvaraḥ guruḥ sākṣāt paraṃ brahma tasmai śrī gurave namaḥ
So God, who is Brahmā, Viṣṇu and Maheśvara, is the true Guru. What is Pūrṇimā? Pūrṇimā is the day your mind is pure, still and selfless, with no faults at all. Whatever is said with a holy heart is truly the word of God. The word that rises from our own heart is the true word of the guru.
Ekalavya's devotion to his guru
One day, as Droṇācārya, his wife and his son Aśvatthāmā were travelling together, they came upon some children at one place, shouting loudly and running around a well. Who were those children? The sons of Dhṛtarāṣṭra and the sons of King Pāṇḍu. Then Droṇācārya went to them: “Children! What are you looking for?” he asked. “We were playing, and our ball fell into this well,” the children told him. Then Droṇa: “Are you taking so much trouble to get this out? I will get it out,” he said, and he took an arrow and shot it. It went straight down and pierced the ball. He took another arrow and shot it so that it pierced that arrow. When he had shot five or six arrows one after another in this way, the ball could be drawn up out of the well. Seeing this wonder, all the children fell at his feet.