Alumbra comes from alumbrar, meaning “to illuminate” or “to light up.” It is more poetic than simply saying ilumina, and in the song, “que alumbra mi corazón” describes the beloved as an angel who fills his heart with light and hope.
"Ángel" switches between Spanish and English, and the two halves tell slightly different stories. The Spanish part is the bold one. He admits "Yo no veo el futuro" (I don't see the future), but he doesn't care: "No pienses en mañana, vamos a amarnos hoy" (Don't think about tomorrow, let's love each other today). It's a live-in-the-moment pitch, and a nice one to learn because "no pienses" is a negative command, the kind Spanish builds with a different verb form than a normal statement.
The English verses are the confession. He tried to forget her, but the light of her eyes still shines "like an angel", and she made him face things he was afraid to show. Back in Spanish he repeats it: "Y, mi vida, yo trataré de olvidarte" (And, my love, I'll try to forget you), then gives up on that idea right away with "Tú eres un ángel que alumbra mi corazón" (You are an angel who lights up my heart). Look out for "mi vida": literally "my life", it is an everyday way to call someone "my love".