After Broly was defeated by Goku and Vegeta as Power Saiyan 4s, because he was not already dead when he was defeated, he was sent to Hell. While he was in Hell, he trained for two years and finally, his anger took control. A red energy feild surrounded him, and it turned in to a red aura. This outburst of power ripped a hole in between Hell and the world of the living. Broly escaped through the rip, and Jeice, from the Ginyu force, secretly followed.
A Legendary True Super Saiyan looks exactly like a Legendary Super Saiyan except it has a red aura.