Martirio literally translates to "martyrdom," but in a more common, less religious context, it means "torment" or "suffering."
In this song, Fidel Rueda uses martirio to express the intense pain and suffering he feels when he's not with the person he loves. He sings, "porque es un martirio que no es usted es junto a mí" (because it's a torment that you are not next to me), highlighting the deep emotional anguish of separation.
Fidel Rueda's "Si Yo No Estoy Contigo" is a dramatic declaration of love and utter dependence. The singer feels a chill in his heart when he's with his beloved, and even feels like he's dying, stating, "siento frío en mi corazón siento que yo me muero" [I feel cold in my heart, I feel like I'm dying]. He can't imagine living without this person's love, proclaiming, "yo no quiero vivir ya sin tu amor" [I don't want to live without your love anymore].
It's a really intense song, where being apart feels like torture. He says, "se me va la vida sin ti" [life leaves me without you] and "es un martirio que no estés junto a mí" [it's a martyrdom that you're not next to me]. He desperately misses everything about them: their warmth, kisses, laughter, voice, skin, face, eyes, and mouth. In fact, he'd rather be dead than far away from them, repeating, "prefiero estar muerto que estar tan lejos de ti" [I prefer to be dead than to be so far from you]. Talk about devotion!