"the sword outwears its sheath"
Byron uses the metaphor of a sword to represent human life. Like a sword, the person is dulled and worn down by use over time, the sword (person) is no longer useful. This metaphor conveys the idea that human life is finite and that one's youth and vitality will eventually fade away.
Also very erotic and phallic suggesting that the sword, the penis, is still active but the sheath, the speakers body is tired