For the sword outwears its sheath, And the soul wears out the breast,
The speaker continues to explain the meaning of his decision to stop roving. He's going to stop roving is because he's tired of it—it's time for him to stop messing around. Enough is enough. That's the gist of it.
The idea of old age becomes even more pronounced here. A sword can only outwear its sheath (its holster or scabbard) after a long time. The speaker is like the sword; he's been around a while and has "worn out" his desire to rove.
(Here's an old beat-up sheath just in case you're interested.)
The same goes for that bit about the soul. Eventually, the soul — an inanimate, inner spiritual being that some say resides within us — gets tired of the body and goes wherever souls go.
This is a very specific reference to death. In many religions, including Christianity, when you die your body remains on earth but your soul goes to heaven or some other spiritual place after life.
"Sheath" and "breast" don't rhyme sonically, but they both contain that "ea" vowel group. This is kind of an example of an eye rhyme — i.e., two words that look similar but don't actually rhyme.
We say kind of because the words don't look that similar (the examples usually given are "slaughter" and "laughter"), but parts of them do.
And the heart must pause to breathe, And love itself have rest.
The speaker continues to explain his meaning. The "heart must pause to breathe" and "love itself have rest."
We have lots of anaphora going on too, what with all those "ands."
Okay, the first bit implies that roving is a tiresome activity—the heart needs to rest. Wait, heart? We thought he was talking about wandering around at all hours of the night?
Well he is. The heart makes things a little tricky. He's probably thinking of the heart in a figurative sense as the source of motivation. For example, when your friend asks you why you no longer play baseball, you might say "my heart's not in it anymore."
Sometimes, the heart needs a break from wanting to do things. If your heart is always obsessed with something, like roving, it can get tiresome.
The speaker is also probably thinking of the heart as the source of love and emotion. This is why he talks about love needing a rest too.
Love eh? Yep. He might just be thinking of some basic kind of love (like a love of French fries, or roaming), but this is Byron. He definitely loved the ladies.
It's entirely plausible that Byron is talking about chasing girls, or loving girls, or something to do with romance. It's still kind of vague, which is probably good.