Less is known about Pythagoras that any other ancient Greek philosopher that I'm likely to cover. Many different things are attributed to Pythagoras, but it's impossible to determine which actually originate with Pythagoras, and which originate earlier or with later members of the school of thought which he established.
He is sometimes described as a mystic, and other times as a man of science. Some associate him with numerology, the idea that numbers have mystical significance. I won't delve into numerology here, but it is interesting. He is probably best known for his supposed advancements to mathematics, including the Pythagorean theorem. However, many if not all of his mathematical discoveries were likely learned from other cultures during his travels. He is also accredited with being one of the first people to teach that the earth is spherical, as well as the first to identify the morning star and the evening star as being the same object (Venus).
In terms of philosophy, Pythagoras's most significant idea was metempsychosis, or the transmigration of the soul. Today we would call this idea reincarnation. Pythagoras believed that all souls are immortal, and that after death souls are transported to new bodies to live new lives. Later Greek authors even implied that Pythagoras claimed to be able to remember several of his former lives, which included a hero in the Trojan war and a fisherman.
A related idea associated with Pythagoras is that there are three different types of souls, which correspond to the three types of people which attend the Olympic Games. Those who comes to compete, those who come to watch, and those who come to sell food and merchandise. Thus the three types of souls are lovers of honor, lovers of wisdom, and lovers of wealth. This is a bit tongue in cheek, but it certainly isn't an inaccurate portrayal of some people.
Pythagoras was represented in Protrepticus, an early work of Aritstotle. "When Pythagoras was asked [why humans exist], he said, "to observe the heavens," and he used to claim that he himself was an observer of nature, and it was for the sake of this that he had passed over into life." This sounds incredibly similar to something that I have said myself in the past. Humans exist in order to perceive and interact with their environment. Any further purpose is theirs to create.