The word Mādrī means 'she who is the princess of Madra Kingdom'.
Marriage To Pandu
Having just ascended the throne, Pandu went to war, conquering or allying with many kingdoms in the name of Hastinapur. When he approached Madra, he found a huge army waiting him. During the war, he found King Shalya's charioteer driving the chariot fast. Shalya revealed that the charioteer was none other than his own sister, Madri. He proposed that the two kingdoms avoided war via marriage. Thus, Pandu married Madri.
Retreat To The Forest
Birth of Children
As Kunti and Madri had sister type relations between them; Kunti whole heartedly agreed to share the mantras with Madri. Thus, Madri bore the twins Nakula and Sahadeva of the Ashwini Kumaras. At their birth, an incorporeal voice from the Heavens declared that the children would surpass their fathers in energy and beauty.
Death Of Pandu & Self Immolation
Once Pandu desired his wife's company, forgetting the rishi' curse and becoming intimate with Madri caused his death. Madri, filled with remorse, went sati on Pandu's funeral pyre.