Alzate wishes he could be every object that gets close to the woman he loves. Her bed, "la funda de tu almohada" (your pillowcase), "la toalla que te abraza" (the towel that hugs you), even "el espejo donde a diario te maquillas" (the mirror where you do your makeup every day). It's a list of increasingly clingy wishes, and he knows it.
Then reality hits: "Pero sólo soy un simple terrenal" (But I'm just a simple mortal). Terrenal means earthly, a regular human down here on the ground, while she's his "princesa" (princess). He even admits to calling her at night and hanging up, "lo sigo haciendo" (I keep doing it), which is a little embarrassing and very honest.
Learner tip: "no quito el dedo del renglón" literally means "I don't take my finger off the line", but it's an idiom for "I won't give up". As long as he lives, he's not letting this go.