What is the "casual comedy" to which Yeats refers in "Easter 1916"?

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.