The original (fairly small) cockroach protests were about the Supreme Court Chief Justice calling unemployed people 'cockroaches'. He apologised, but it led to the formation of a satirical group called 'Cockroach Janata Party' (Janata = People, and a reference to the ruling Bharatiya Janata Party).

The first big protest the CJP was involved in was about the National Testing Agency (which conducts many university entrance tests) f***ing up repeatedly and leaking question papers. Following those protests the union Education Minister resigned.

The current protests are against Chief Election Commissioner Gyanesh Kumar removing millions of voters from the electoral rolls. At first he was doing it 'legally', by arguing that these records had insufficient documentation / spelling mistakes / mismatches (more likely to happen for poorer / rural people, who are also less likely to vote for the BJP) but then it was revealed that he was doing this behind the backs of the two other election commissioners (so against the legally binding majority opinion) and that he had requested a popular civil servant to contest for the BJP (that guy refused).

That was over exam fraud. The education minister resigned which was the goal so that protest ended. This protest was started by both the federal opposition party and the roach protestors on Sept 24.