Origin of the term
The Latin word militans has a primary meaning of “serving as a soldier, military”, but it acquired a secondary meaning of “to struggle, to make an effort”, which is the intended sense here. Christians on earth (the Church Militant) are still struggling against sin in order that, when they die, they might go to heaven and be members of the Church Triumphant, those who have triumphed over sin. However, if this struggle is successful, but not completely so, then after death they temporarily become members of the Church Suffering before ultimately joining the Church Triumphant.