Dragon Ball Z is all about The Z-Fighters of earth, protecting the planet from destruction at the hands of such as Vegeta, Raditz, Freiza, And Dr. Gero's Androids.
In Dragon Ball Z, Gokuu(introduced in DB), is now a married adult with a half-sayi-jin son named Gohan. The first fighter to arrive is Raditz. Followed By Vegeta And Nampa. Then, everyone ships off to planet Namek! Home Of The Green Guys!! To Collect Some Dragonballs. They end up leaving Gokuu on the planet, and heading back to earth. Gokuu beats the crap out of Frieza, the Head BadGuy, and heads back to earth, while Gohan, Piccolo, Kliln, and Kame try desperatley to save the earth from Garlic Jr.
Then, "A Mysterious Youth" comes from the future to tell Gokuu about 2 (which turns out to be 4 or 5) androids that will destroy everyone, everywhere, and about a heart disease that will kill him.
Three years pass, and the fight begins...
Gokuu Starts Beating the crap out of A Big Fat Android With A Girly Man's Voice, when the heart virus attacks him...
I could tell you more, but we're close enough to the current episode to let you watch it yourself.=)