Postcolonial describes the time period after Western nations left the nations they colonized and ruled. After the end of British rule, Jawaharlal Nehru became India's first postcolonial leader.
The adjective postcolonial can refer to the specific era following the end of a colonial regime, when a powerful empire that's taken over other lands withdraws from them. It's also used for the project of investigating how people and land have been affected by the colonizer, even years later — there are whole genres of postcolonial literature and art, for instance. Post means "after," and colonial comes from the Latin colonia, "settled land."