The Soviet invasion into Czechoslovakia happen a year earlier, in the violent Communist suppression of the "Prague Spring" in Czechoslovakia, the relaxation towards the Czechoslovakian people by the leader of those days, Alexander Dubček. Soviet tanks then invaded the city, under direct orders from Moscow, and abolished the relative freedom allowed by the Czech regime and later ousted the leader.
Palach's funeral in Prague was for a leader demonstrator in the mass public protest of the Soviet invasion, opposing the strict Communist rule, that was controlled from Moscow. A month after Palach's stunt, another student set himself on fire as well, named Jan Zajíc. Later, another patriotic youth also set himself on fire in the city, Evžen Plocek.
The shock that this suicide brought, mostly to the free and democratic Western world, was not felt by the Soviet occupier, that was not affected by the arson operation and did not weaken its stand in the slightest.