The story of Piccolo is a strange one, but I'll do my best to explain it the way I understand it. It all started with Piccolo's father - Piccolo Demieho. He was a young and genius Namek, capable of creating the Dragonballs. He had spent many years and earth, and all the violence and hate had a devastating effect on him. So, using an old Namek fusion trick, he split himself into 2 separate entities - Kami (who was good and became Guardian of the Earth) and Piccolo Demieho, who was bent on doing more evil and wrong. They were joined to each other by the mind, so if one died, the other could not continue to live.
Demieho soon met his match in Goku, who killed him. Before Demieho died, he spat out an egg filled with his thoughts. From this egg, Piccolo Daimao was hatched, and from his thoughts, he shared his father's hatred for Goku and was determinded to kill him as an act of vengeance. Goku and Piccolo were arch-rivals, always competing and fighting. When the Saiyan, Radditz, came to Earth they were forced to make an unlikely bond in order to defeat him. In doing so, Goku sacrificed his life as Piccolo shot a Special Beam Cannon through both Goku and Radditz to ensure the Earth's safety. When the warning comes of two more Saiyans on their way - Vegeta and Nappa - Piccolo takes Gohan, Goku's son into training for the battle. In the wilderness, Piccolo and Gohan become good friends, and Gohan admires Piccolo and looks up to him. In the battle with the Saiyans, Piccolo chooses death in order to save Gohan, and in doing so, kills Kami and the Dragonballs. While in the other dimension, Piccolo trains hard under King Kai and as a result harnesses massive power. Piccolo is wished back to his homeplace Namek to fight Frieza, a feared and powerful fighter. It is here where he joins with Nail, another Namek trained in the ancient way of fighting using the same fusion technique his father used in splitting himself. With Nail's power combined with Piccolo, the single-bodied duo have enormous power. Although their combined power is not enough to beat Frieza, Piccolo survives the fight to make it back to Earth with the other Nameks. Later on, the Nameks leave Earth in search of a new homeland, but Piccolo chooses to stay behind with Gohan and the others.
In doing so, Piccolo receives word of two massively powerful Androids that will arrive on Earth in 3 years time. He soon goes into training with Gohan and Goku, and again increases his potential. The Android Saga has begun, and the outcome is awaited.