When the British conquered the Buddhist kingdom of Burma, Buddhism lost the protection it had from the king. The laity then organized in order to defend their Buddhist institutions, and people began to study the dhamma like never before.
This gave rise to talented monks who preached to the laity. Then Ledi Sayadaw, a Burmese monk, began preaching that meditation was not something that only monks who dedicated their lives to it could do, but was available to anyone. This led to a lineage of lay teachers of meditation, one of whom was Goenka, the founder of the Vipassana meditation movement.
In short, the modern Vipassana movement has its origins in the popularization of meditation which was a result of British colonialism in Burma.