Armus himself tells Picard what he is. He was a by-product of a procedure in which a race of "titans" brought out from within themselves all evil and negative attributes that had bound them to destructiveness.
Here is what Armus said of himself to Troi:
TROI: And the emptiness remains. You sound so alone.
ARMUS [OC]: I am alone.
TROI: Abandoned. Who deserted you?
ARMUS [OC]: Creatures whose beauty now dazzles all who see them. They would not exist without me.
TROI: You were together?
ARMUS [OC]: They perfected a means of bringing to the surface all that was evil and negative within. Erupting, spreading, connecting. In time it formed second skin, dank and vile.
ARMUS [OC]: Yes.
TROI: They discarded you and left.
ARMUS [OC]: And here I am.
Here is what Armus said of himself to Picard:
PICARD: How long have you been here?
ARMUS: Since they left. A very long time.
PICARD: A long time to be alone.
ARMUS: Save your compassion. It's revolting. You offer it like a prize when in fact it's an insult.
PICARD: Because you feel unworthy.
ARMUS: You overrate your gift. You humans are puny, weak.
PICARD: But our spirit, it is indomitable.
ARMUS: And still you die from a flake of my power.
PICARD: A great poet once said, 'all spirits are enslaved that serve things evil'.
ARMUS: You do not understand. I do not serve things evil. I am evil.
PICARD: Oh, no, you are not.
ARMUS: I am a skin of evil left here by a race of Titans who believed if they rid themselves of me, they would free the bonds of destructiveness.
Given these descriptions and the creatures demonstration of power, Picard would reasonably assume that the embodiment of evil and malice would effectively be immortal.