The two staffs (or other objects held) generally represent the male and female, or other dualities. For example, there are depictions where in stead of staffs the deity is holding Spondylus and Strombus shells, known symbols for male and female.
The Inca prayer to Viracocha contains several of these dualities:
Viracocha, Lord of the Universe!
Whether male or female,
at any rate commander of heat and reproduction,
being one who,
even with His spittle, can work sorcery,
Where art Thou?
Would that Thou wert not hidden from this son of Thine!
He may be above;
He may be below;
or, perchance, abroad in space.
Where is his mighty judgment-seat?
Hear me!
He may be spread abroad among the upper waters;
or, among the lower waters and their sands
He may be dwelling.
Creator of the world,
Creator of man,
great among my ancestors,
before Thee my eyes fail me,
though I long to see Thee;
for, seeing Thee,
knowing Thee,
learning from Thee,
understanding Thee,
I shall be seen by Thee,
and Thou wilt know me.
The Sun--the Moon;
The Day--the Night;
Summer--Winter;
not in vain,
in orderly succession,
do they march to their destined place,
to their goal.
They arrive
wherever
Thy royal staff
Thou bearest.
Oh! Harken to me,
listen to me,
let it not befall
that I grow weary
and die.