Alumbrar means "to illuminate" or "to light up." While it can refer to literal light, it often carries a more poetic and metaphorical sense.
In this song, Tona La Negra uses alumbrar to express how the beloved person lights up their hopes and dreams: "Has de alumbrar mi ilusión" (You must light up my illusion/hope). It's a beautiful way to describe the profound impact someone has on one's inner world.
The song is built on a conditional the singer never gets an answer to: "Si me pudieras querer / Como te estoy queriendo yo" (If you could love me / the way I am loving you). Everything before it is her case for why the answer should be yes. Someone "Despertaste nueva vida en mí" (woke a new life in me) and she wants that person to stand as "faro de mi querer" (a lighthouse of my love), steady enough to light up something she herself calls an illusion: "Has de alumbrar mi ilusión". What she actually asks for is small and physical — "Los besitos de tu boca / Que mejor me hacen vivir" (the little kisses of your mouth that make me live better).
Then she says the objection out loud instead of leaving it unspoken: "Que nunca me podrás amar / Porque la vida no quiere y nada más" (that you will never be able to love me, because life does not want it, and that is all). Her reply is to appeal over life's head — "Deja que Dios o que el destino quieran / Y entonces la vida también lo querrá" (Let God or destiny want it, and then life will want it too). It is the one move the song makes, and it is an old bolero move: if the higher court rules in her favour, the lower one has to fall in line.