If you’re very busy, what noun do you use to describe the state you’re in? Would it be… busyness? No, that doesn’t look or sound right, does it? It’s kind of uncanny, because it sounds like business, but it isn’t, and it looks weird with the Y before the suffix -ness.
But odd as it might look and sound, it’s correct. That, however, is actually a fairly recent development. In fact, for much of the history of English, business was the noun form of the adjective busy. This makes sense: lots of abstract or general nouns end in -ness, and if the word they’re formed from ends in Y, that usually gets changed to I. This is mainly because Y sort of falls between being a vowel and a consonant, and because of its consonantness, we tend to avoid using it like a vowel in the middle of words.
But over time, the meaning shifted, and it came to mean commmerce, or affairs in a more general sense (the modern pronunciation, with just two syllables, is from the 17th century). It’s not such a huge change, just becoming a little more specific really, and not generally associated with the idea of being busy.
This of course then left a little gap in the language, to be filled with a noun form of busy. There was no real pressure to fill this gap though, because how often do you need to use the noun form of busy? The word busyness therefore wasn’t first used (with this spelling) until 1849, and it hasn’t been used much since (have you ever used it?)
Still, as niche as its meaning is, it’s good to know it’s there if you ever need it.