Kumar was born into a political family of Dalit (formerly untouchable; now, officially, Scheduled Caste) origin. She completed B.A. and M.A. degrees in English literature and an LL.B. from the University of Delhi.
In 1973 Kumar entered the Indian Foreign Service, where she served for more than a decade. After postings to Madrid and London, she decided in 1985 to enter politics, encouraged by her father and by Rajiv Gandhi, then prime minister of India. She ran in a by-election for a seat in the Lok Sabha from Bijnor constituency in Uttar Pradesh state, defeating two other Dalit candidates—one of whom, Kumari Mayawati,
Being close to the politically powerful Gandhi family and representing the lower castes, Kumar’s political career progressed steadily within the Indian National Congress (Congress Party). In 1991–92 she served as the general secretary of the All India Congress Committee. She was again chosen for the post in 1996 and remained in office until 1999. In addition, she twice served (1991–2000 and 2002–04) as a member of the Working Committee of the Congress Party, the organisation’s highest decision-making body.
She resigned from the Congress Party in 2000, citing differences with the party leadership, but rejoined it two years later. In 2004 and 2009 she contested and won the Lok Sabha seat from Sasaram in Bihar state, the constituency once represented by her father.
As a speaker, Kumar launched several initiatives within the Lok Sabha, including one in 2011 designed to reduce the amount of paper used in the house. Under its provisions, all Lok Sabha members were issued tablet computers. Kumar also lent her support to the growing nationwide movement opposing violence against women in the country. She left the speaker’s post in June 2014, following the expiration of her term.