Indomable means "untamable" or "indomitable". It's a powerful adjective used to describe a wild spirit that cannot be controlled or subdued.
In this bachata, Romeo Santos describes his past self as a salvaje (savage) but then confesses, "Y este salvaje no fue indomable" (And this savage was not untamable). He uses this word to reveal that while he seemed impossible to conquer, his lover's affection was the one thing that could finally tame his heart.
Romeo Santos is here to make a big confession. He starts by saying he finally understands something important: "Logro entender / Que yo siempre he sido tuyo" (I manage to understand / That I have always been yours). He admits he's been with other people, describing it as "alquilando mi piel" (renting my skin) while he had the perfect woman right beside him. He doesn't make excuses, just says it was a mistake that fed his ego.
But the main point of the song is his total devotion now. He's done playing around. He declares over and over, "Yo soy tuyo y de nadie" (I am yours and nobody else's). He even calls himself a "salvaje" (savage) that she was able to tame. It's a dramatic apology and a promise that from now on, it's just "Tú, yo y nadie más" (You, me, and nobody else).