Piccolo originated on Planet Namek, but was sent to Earth by himself as a child. Being completely alone he was psychologically scarred by the tumultuous incidents and wars on the Earth.
The internal torment Piccolo suffered caused him to split into two people. One contained the good attributes, this became Kami the guardian of Earth. The stronger, more evil part retained the name Piccolo.
Piccolo was determined to take over the Earth, his only real competition on the planet was Goku, also not originally from Earth.
In Dragon Ball Z, at the time Raditz came to Earth in order to retrieve Goku. Piccolo joins forces with Goku and the other Z Fighters, in order to defeat their common enemy. Goku sacrifices himself to defeat Raditz, Piccolo firing the fatal shot.
Piccolo takes Goku's son, Gohan, to train him to defeat the new lot of Saiyans who were going to come to Earth in the near future. His training style is very rough, and forces Gohan to fend for himself. Piccolo spars with Gohan violently. The two develop a close relationship.
To increase in strength, Piccolo fuses with Nail while on Namek to better fight Frieza. He later re-fuses with Kami to become more powerful, when it is necessary to defeat the Android Cell.
Piccolo stays on Earth instead of going back to Namek, as he does not feel a part of that planet. By staying on Earth he can watch over Gohan while his father is away.