These terms are often used in the context of the doctrine of the Communion of Saints; although Christians may be physically separated from each other by the barrier of death, they nonetheless remain united to each other in one Church, and support each other in prayer.
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.
The Roman Catholic Church commemorates the Church Triumphant and the Church Suffering on two consecutive days: All Saints Day on November 1 (the Church Triumphant), and All Souls Day on November 2 (the Church Suffering).