Dragon Ball Super movie:Broly was the son of a low-class Saiyan warrior, yet even as an infant he displayed an abnormally high combat potential. For this reason he was placed in the highest priority Saiyan nursing facility, something which King Vegeta did not take kindly to. Having a commoner in the same room as his son was a disgrace to him, even more so after he personally witnessed the insane potential Broly held. Out of both wounded pride that his son had been overtaken and fear that Broly may one day turn against them, King Vegeta ordered Broly to be exiled to Vampa, the most remote and barren planet he could find, in hopes that he would simply die a quiet death. Outraged, his father Paragus steals a ship and heads to Vampa to rescue Broly. But after the ship is irreparably damaged from a crash landing they are forced to stay there indefinitely. It isn't until 40 years later that the two are finally recovered by a stray Frieza Force vessel, re-inducted into the army, and then immediately set upon Vegeta and Goku.
Original Broly movies:
Broly was the first Legendary Super Saiyan born in more than a thousand years. At birth, he had an unusually high level of strength for a Saiyan. Broly's exceptional gifts marked him as possibly being the Legendary Super Saiyan. King Vegeta feared this and ordered for his execution. His father, Paragus, begged to spare his life. King Vegeta ended the argument by blasting him. As Broly's execution was carried out both he and his father were left to die. While Paragus barely survived the blast, Broly survived the attempted execution only to grow stronger. On that same day, Frieza acted on his own fear of the Super Saiyan legend and attacks Planet Vegeta. Amid the destruction, Broly encased himself and his father in a powerful shield of energy and escaped. As great as Broly's power was, his emotional instability was greater. Fearing Broly's state of mind, Paragus had a scientist create a special control device to keep Broly controlled. Successful in controlling him, Paragus planned to have revenge on King Vegeta's son. When Broly encountered Son Goku, Broly became erratic though he was brought back under control by Paragus. Eventually, Broly overpowered the control device, and fully manifested his powers. No longer under the device's control, he unleashed his fury on Goku, Vegeta, Son Gohan, Future Trunks, and Piccolo, and defeated them all. The Z warriors eventually channeled their energy into Goku, who used the energy for one last powerful blow that seemingly killed Broly. Broly survived and entered a Saiyan Space Pod, coincidentally landing on Earth. The crater caused by his landing filled up with water and froze over time, during which he fell into a deep sleep. During this time, Gohan grew up, Son Goten was born and Goku was in the Afterlife. In an adventure to collect the Dragon Balls, Goten, Trunks, and Gohan find themselves in the mountain range where Broly crashed. Broly awakens and Goten, Trunks, Videl, and Gohan became victims to his rampage. It was only after some spiritual help from Goku that they were able to send Broly straight into the sun. (Source: Wikipedia)