Cassius' belief, expressed to Messala, suggests that the seeming coincidences and omens he sees around him might actually presage some doom to follow on the battlefield. Cassius begins by telling Messala
This is my birthday, as this very day
Was Cassius born...
You know that I held Epicurus strong,
And his opinion. Now I change my mind,
And partly credit things that do presage.
Cassius' birthday is an ominous omen of his death day (oddly - of course - Shakespeare died, we think, on his own birthday). Epicurus did not believe in godly interference, but in the power of humans to shape their own destiny - and the superstitions Cassius here credits would be distinctly unEpicurean. This is a different Cassius from the anti-superstition one in the thunderstorm in Act 2.
Cassius describes how two eagles flew around their army, but have now flown away, to be replaced by
...ravens, crows, and kites
Fly o'er our heads and downward look on us,
As we were sickly prey. Their shadows seem
A canopy most fatal, under which
Our army lies, ready to give up the ghost.
This is a Cassius who credits superstitions, omens and prophecies: quite different from his earlier Epicurean behaviour. And does it have something to do with his suicide? Undoubtedly. Before he kills himself, he says:
This day I breathed first: time is come round,
And where I did begin, there shall I end:
My life is run his compass.