According to Wikipedia,
The Guru Purnima celebration is marked by ritualistic respect to the guru, Guru Puja. The Guru Principle is said to be a thousand times more active on the day of Guru Purnima than on any other day.
In the yogic tradition, the day is celebrated as the occasion when Shiva became the first guru, as he began the transmission of yoga to the Saptarishis. The story goes that over 15,000 years ago, a yogi appeared in the upper regions of the Himalayas. Nobody knew what his origins were. But his presence was extraordinary, and people gathered. However, he exhibited no signs of life, but for the occasional tears of ecstasy that rolled down his face. People began to drift away, but seven men stayed on.
When he opened his eyes, they pleaded with him, wanting to experience whatever was happening to him. He dismissed them, but they persevered. Finally, he gave them a simple preparatory step and closed his eyes again. The seven men began to prepare.
Days rolled into weeks, weeks into months, months into years, but the yogi’s attention did not fall upon them again.
After 84 years of sadhana, on the summer solstice that marks the advent of Dakshinayana, the earth’s southern run, the yogi looked at them again. They had become shining receptacles, wonderfully receptive. He could not ignore them anymore.
On the very next full moon day, the yogi turned south and sat as a guru to these seven men. The Adiyogi (the first yogi) thus became the Adi Guru. Adiyogi expounded these mechanics of life for many years. The seven disciples became celebrated as the Saptarishis and took this knowledge across the world.
Guru Purnima is held sacred in the yogic tradition because the Adiyogi opened up the possibility for a human being to evolve consciously. The seven different aspects of yoga that were put in these seven individuals became the foundation for the seven basic forms of yoga, something that has still endured.
Many Hindus celebrate the day in honor of the great sage Vyasa, who is seen as one of the greatest gurus in ancient Hindu traditions and a symbol of the Guru-shishya tradition. Vyasa was not only believed to have been born on this day, but also to have started writing the Brahma Sutras on ashadha sudha padyami, which ends on this day, which is also known as Vyasa Purnima. Veda Vyasa, did yeoman service to the cause of Vedic studies by gathering all the Vedic hymns extant during his times, dividing them into four parts based on their use in the sacrificial rites, and teaching them to his four chief disciples – Paila, Vaisampayana, Jaimini and Sumantu. He divided the Veda into four, namely Rig, Yajur, Sama and Atharva.
Vyasa also wrote the Mahabharatam, Shrimad Bhagwatam and the 18 Puranas.