Big Barda is a New God a former Female Fury and later wife of Scott Free a.k.a Mister Miracle.
Barda is a New God, a race of cosmic entities that have been waging war on Earth. She was raised on the cruel and destructive planet Apokolips and trained to be commander to the Female Furies, an all-female team of super-powered mercenaries that serve Darkseid.
Barda and Scott met shortly before his escape from Apokolips. Scott's gentle nature and free spirit inspired Barda to defect from Apokolips and follow him to Earth. They later married and joined the Justice League. There aren't too many people that can get close to Big Barda, but the ones who do often manage to see beyond her hard exterior lies a woman longing for the simple life.
Big Barda, along with many other New Gods, was killed by the Infinity Man, Darkseid's brother. Mister Miracle, distraught at losing his one true love, sought revenge on her killer, only to die in vain. She was later shown reincarnating on a parallel Earth along with several other New Gods.