A boon is a good thing and a bane is a bad one - both of them are fairly unusual words, and I've never heard that expression before. It is very rare indeed. Where did you find it?

They aren't customarily paired. It's a clever pairing, someone's invention. Neither of them is basic core English vocabulary. Their meanings are not precisely opposites. They are both a little old-fashioned-sounding, the sort of thing you might expect in a "swords-and-sorcery" fantasy book. A boon means a gift, a blessing, a benefit. A Chloës notes, there's a stock phrase, "a boon to society." Antibiotics are a boon to society. A bane means something that ruins or spoils something else. It's most commonly encountered as part of the English names for plants that are poisonous to something. Henbane, dogsbane, wolfsbane. You could say "a bane to society" and it would make sense but, unlike "a boon to society" it isn't an idiom and it doesn't sound quite right to me. I AM WRONG: Google Books is showing me 18,000 hits for "boon to society" and 4,000 for "bane to society" so I guess "bane to society" is legitimate, and more common than I thought. 1911, "the thoughtless woman is just as much a bane to the home as she is a bane to society."

The phrase is not used in everyday conversation. You might read it in a newspaper. The phrase is used to talk about opinion in politics or culture. "Is (the thing) a boon or bane to society?" = "Is (the thing) good or bad for society?"