Planet Vegeta (formerly, known as Planet Plant) was the home of the Saiyans before is was destroyed by Frieza. It is named after the king of the Saiyans, King Vegeta.
Planet Vegeta was known as Planet Plant before the Saiyans took it over when the once-in-300-years full moon came along and they all transformed into Great Ape and wiped out the only other race on the planet, the Tuffles.
After witnessing Bardock's elite wipe out planet Kanassa, Frieza became worried that a Super Saiyan (a Saiyan with unbelievable power) might overpower him, so he decided to exterminate the Saiyans. Bardock found this out and tried to raise a Saiyan army to stop Frieza, but none listened. He then went up to face Frieza in space. He charged up his most powerful attack, but it was completely consumed by Frieza's massive Death Ball. He threw the ball and destroyed the planet and all but 8 Saiyans (four in manga canonicity) survived.
Planet Vegeta before it's destruction