The quote you are refering to comes in the second stanza of this brilliant poem, in which Yeats explores his ambivalent thoughts about the Easter uprising in Ireland in 1916. The poem begins by establishing the dissatisfaction of the speaker with the way that Ireland was before the uprising. Ireland is depicted as consisting of "grey / Eighteenth-century houses" and where future revolutionaries are made fun of and greeted by "Polite, meaningless words." The second stanza then moves on to describe certain individuals who were involved in the uprising. It is the description of one of these characters that results in the quote you refer to:
He, too, has resigned his part
In the casual comedy...
Thus we can see that the "casual comedy" of this line refers to the existence of Ireland and the unsatisfying, bleak way of life of the people before the Ireland. "Resigning" his place in this "casual comedy" thus indicates the intention of this anonymous individual to protest against it, becoming involved in the uprising that gives rise to the "terrible beauty" of the rebellion.