a breaker: a crashing, engulfing wave of the sea at its most overpowering
This word names a wave, but never a gentle one. It is the towering breaker, the wall of water that crashes down and swallows a person whole. It shows up only five times in the Hebrew Bible, always in poetry, and always at a moment when someone is going under: drowning in fact, in feeling, or in the imagined depths of death itself. The English word "wave" is almost too mild for it; picture instead the sea at its most terrifying.
One word does two very different jobs here, and the poets signal which by a small grammatical turn. Sometimes the breakers belong to hostile powers, the waves of Death or of the raging Sea, and God overpowers them. Sometimes they are called "your breakers," and they belong to God himself, sent sweeping over the sufferer. The same crashing water that God is praised for conquering can also be the very thing he sends against a person in dark providence.
That second use is the more startling. When the drowning speaker says "your breakers passed over me," he is not blaming bad luck or blind nature. He is telling God, to his face, that the flood is God's own doing. Jonah, actually thrown into the actual sea, borrows those exact words from a psalm of lament: the poetic picture has become his literal situation.