Rukmini was the eldest of Krishna'S eight wives. The other seven were
(In Mousala parva, Shybya, Gaandhaari and Hymavathi were also mentioned as Krishna's wives. Details about these are not known.)
She was the daughter of Bheeshmaka (note, not Bheeshma, the grandsire) who was the king of vidarbha provinces. She had five brothers, the eldest of whom was Rukmi.
Rukmi was a friend of Chedi king Shishupaala who was Krishna's maternal cousin. As such, he decided to give rukmini to Shishupaala in marriage, though he knew that Rukmini loved Krishna and wished to mwrry him.
Rukmini did not like her marriage with Shishupaala and she sent a word to Krishna to come and take her away. Krishna went accordingly and abducted her before all the kings. Naturally, all the kings challenged him but were defeated. But, Rukmi alone chased Krishna and challenged him toa fight. Krishna defeated Rukmi and thouroughly insulted him by shaving his head unevenly. Rukmini prayed to Krishna to leave her brother alive.
She had a son Pradyumna, who along with Saathyaki, taught archery to the junior paandavas and abhimanyu.
The story in the Harivamsham about Krishna's bringing the divine tree Paarijaatham for Sathya and Rukmini's involvement in that is a famous subject of many poetical works . However, her role in Mahaabhaaratham is very less .
After Krishna's leaving this world, Arjuna took her alongwith other women and Dvaaraka's population to Kurukshethram. There he told her about Krishna's departure. She heard the news with dignified frief and immolated herself to death.