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
She, alongside Kunti, faithfully accompanied Pandu in his hermitical retreat following his abdication as the king of Hastinapura. One day, while hunting in the forest, Pandu accidentally shot an arrow killing what he thought was a deer, but was actually the coupling Rishi Kindama. The sage cursed Pandu that he would die when he became intimate with a woman. Both Kunti and Madri were directly affected by the curse on Pandu because they were now unable to bear Pandu's children. However, a boon given to Kunti by Durvasa, enabled her to call upon any God to bear her a child. Accordingly, Kunti called upon Dharma, Vayu and Indra and bore Yudishtira, Bhima and Arjuna respectively. This greatly relieved Pandu.
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, committed sati by immolating herself on Pandu's funeral pyre.