Caiga means "falls", but it's a special form of the verb 'caer' (to fall) called the subjunctive mood. It's used here to talk about a hypothetical, but possible, event: "aunque... el cielo caiga" (even if... the sky falls).
This dramatic and poetic line shows the singer's unwavering devotion, promising to stand by his love no matter what happens. Learning the subjunctive is a major step in mastering Spanish, and this song uses it to create a powerful, unforgettable image.
Prince Royce takes a classic song and makes it completely his own with this beautiful bachata version. The message is simple but so powerful: as long as you have someone you love by your side, you can handle anything. He sets a scene of a dark night, "When the night, has come and the land is dark", but he's not scared. Why? "Just as long as you stand, stand by me." He mixes English and Spanish throughout the song, which feels so natural and personal.
He really raises the stakes, saying that even if "las montañas o el cielo caiga" [the mountains or the sky falls], he won't worry or even cry, "No lloraré, no lloraré / I won't share a tear". All his strength comes from knowing his person is there, "junto a mí" [next to me]. It's a huge declaration of trust and love, saying that one person's presence is enough to make all fears and disasters feel small.