Hagoromo was a monk, he was the son of princess Kaguya Ōtsutsuki who ate the Shinju's forbidden fruit and gained the power to stop armies, a power that he and his brother Hamura would inherit when she conceived them.
The God Tree, Shinju, was angry however and came to take back its power, so Hagoromo and his brother used their power to stop the Shinju by sealing it in Hagoromo. (Unbeknownst to them, however, it was their own mother, fused with the Shinju, that they battled and sealed, but before this, Kaguya created Black Zetsu to facilitate her revival.) People then worshiped him as a god and he created his own religion, Ninshū, the Ninja Creed, and taught it to people in order to better their lives and bring peace to the world.
He also had two sons of his own, the elder son named Indra, who inherited Hagoromo's spiritual energy and the power of his eyes, and his younger son Ashura, who inherited his physical energy and the power of his body. As a result, the two sons were exact opposites. While the elder one was a genius from birth and could do everything on his own, the younger one was much weaker and had a rough time trying to excel in life. The younger son then welcomed the cooperation of others and forged strong bonds with them, then through hard work, he was able to attain a power equaling that of his older brother.
Sadly he began to die before he could achieve his dream and he decided to entrust one of his sons to continue his dreams. Indra believed that peace could only be attained through might, while Ashura believed peace could be achieved through love, and with that Hagoromo chose Ashura to carry on his legacy and lead the people. Then finally, realizing that his death would release the Shinju back into the world, he divided its chakra into nine pieces using the Creation of All Things technique, forming the Bijū, and he created the moon which trapped Shinju's lifeless husk inside of it.
He then left a stone tablet that contained his writings on how to prevent the recreation of the Rinnegan in Indra or any of his descendants, since he feared that such an event would happen someday. It can only be fully deciphered by one who possesses the Rinnegan, another dōjutsu like the Sharingan or the Mangekyō Sharingan can only read a small portion of it. However, unknown to him, the tablet was taken and rewritten by Black Zetsu in order to manipulate Indra's descendants into recreating the Rinnegan, casting the Infinite Tsukuyomi, and resurrecting Kaguya, as was his mission.
However, after his death people turned Ninshū into a weapon and used it to wage war against each other. On top of that, due to Black Zetsu's machinations, his older son attacked his younger son out of jealousy, believing that he was Hagoromo's rightful heir. This formed a rivalry between them and their descendants, the Uchiha and the Senju, that spanned centuries. Ultimately, Hagoromo and his accomplishments were eventually considered fairy-tales and fell into legend.
In spite of his death, his powerful chakra, along with his consciousness, still lived on, and continued to watch over the world for centuries. He met Naruto and Sasuke, and bestowed unto each of them half of his power.
Powers and Abilities
Hagoromo was the first to discover ninjutsu and taught its usage to others, the first he was known to have created was a fūinjutsu to seal Shinju within himself to imprison it and subsequently gained it's powers. This is the same seal that's used currently to seal the Bijū.
He also possesses the Rinnegan that lets him see chakra and gives him access to all 6 chakra types: Katon, Fūton, Raiton, Doton, Suiton, Onmyōton. In addition, it's most notable abilities are its gravity manipulation, body modification, telepathy, summoning, chakra absorption, and resurrection; each based on one of the 6 paths of Buddhist reincarnation from which he derives his title.
As a Rinnegan user, and as a Jinchūriki of the Ten-Tails, Hagoromo had the ability to form Truth-Seeking Balls, which are composed of the five basic chakra nature types, along with Yin-Yang Release.
In the Anime, he awakened the Sharingan eye after witnessing the dead body of Haori that was attached to the God Tree. Unlike the Uchiha who would come after him, however, he awakened it with all three tomoe.
He also learned Sage jutsu from Gamamaru, who trained him at Mount Myōboku. Even before the official training began, he could already sense the presence of natural energy all around him.
He also possessed Banbutsu Sōzō (Creation of all Things), a jutsu that allowed him to use his spiritual energy to make forms and then use physical energy to give those forms substance; literally turning fantasy into reality. He used this jutsu for many things, including creating the Bijū from the chakra of the Ten-Tails.
In addition, Hagoromo was said to possess five sacred treasured tools which would come into the possession of two of his suspected descendants, the Gold and Silver Bros. Three of the items work together to seal people: the "Golden Canopy Rope" paralyzes and extracts the soul upon contact, the "Seven Star Sword" cuts the soul free and curses it, and upon activating the curse the "Crimson Gourd" absorbs the person whole; the curse being not to say the word you use the most, although you'll also be sealed if you remain silent for too long or say words that sound like your most used word. Another item is the "Banana Palm Fan," capable of releasing any of the five elements with a swing, and finally there's the "Amber Purifying Pot" that's capable of sealing someone by getting them to respond to you.
The drawback to these items is that they require a large amount of chakra to use, and prolonged use would kill an average person. Madara Uchiha spat out the Pot and the Gourd after becoming the Ten-Tails' Jinchūriki.