Goku is a saiyan that was sent to earth as a baby boy to destroy it. An oldman named Gohan found him. Goku bumped his head and forgot about his mission. Before Gohan died, Goku called him grandfather.
After many years, Goku's real brother, a saiy-jin named Radditz came to Earth and tried to bring Goku back with him.
So Radditz took Gohan(Goku's son, named after his granfather)to make Goku come.
After fixing that problem and many other adventures and meeting different enemies and allies, Goku became a Super Saiy-jin, then SS2, SS3, and Super Saiy-jin 4.
He is the strongest person in the Univers.
And by the way, Goku is NOt the legendary Super Saiy-jin! Brolli is! He's the guy on my front page kicking.
The difference is that Goku came to a Super Saiy-jin by rage, and Brolly was born a Super Saiy-jin.