Presintió comes from the verb presentir, meaning 'to have a premonition' or 'to foresee'. It's a more evocative and less common word than simply 'knew'.
In the song, the singer laments, "mi alma lo presintió" (my soul foresaw it), referring to the impending departure of his loved one. This word adds a layer of dramatic irony and emotional depth, suggesting that deep down, he always sensed this heartbreak was coming.