According to the Mahabharata, he was the son of Satyavati, a ferryman's daughter, and the wandering sage Parashara. This was before Satyavati’s marriage to Shantanu and before Devavrata became Bhishma. (See here)
Vyasa was born on an island in the river Yamuna. This is said to be near Kalpi in Jalaun district in Uttar Pradesh. He was dark in colour and hence may be called by the name Krishna कृष्णा (black), and also the name Dwaipayana द्वैपायाना , meaning 'island-born' (Dweep = island)
Hindus traditionally hold that Vyasa categorised the primordial single Veda into four. Hence he was called Veda Vyasa, or "Splitter of the Vedas," the splitting being a feat that allowed people to understand the divine knowledge of the Veda. The word ‘vyasa’ means ‘analyze’.
Vyasa is traditionally known as author of Mahabharata (see here). Vyasa was closely related to the Kauravas and Pandavas, so much as that he perpetuated their race in the line of the Kuru king Vichitravirya (although there are doubts whether it was the same Vyasa).
It is said that both Dhritarashtra and Pandu, adopted as the sons of Vichitravirya by the royal family, were born from him. Thus he was the grandfather of the Pandavas and Kauravas. This kinship enabled him to know much about the happenings in the royal family, ultimately enabling him to author their history in the form of Jaya (the original name of Mahabharata). He also makes occasional appearances in the story as a spiritual guide to the young princes.
It is said that he lived in Kurukshetra (see here), in a forest, very near to the battle field, enabling him to know considerable details about the Kurukshetra War, as it took place in front of his eyes. It is said that he continues to live thus.
The Vishnu-Purana suggests that Vyasa is an incarnation of Vishnu and in every third world age (that is, Dvapara yuga - see here for a discussion about yugas), he divides the Veda, which is properly but one, into many portions - fourfold to be exact. This he does in order to promote the good of mankind.