Sorry for late answer.
First of all, both "미혼" and "비혼" are translated as "single" in English. And the context below is explaining the difference between these two words; 미혼 and 비혼.
So in translation, I will just use the original Korean words to distinguish those two.
미혼이라는 말에는 결혼은 꼭 해야 하는 것이지만 아직 하지 않았다는 뜻이 포함되어 있다.
= the word '미혼(Mi-hon)' includes the meaning that someone will have to be married eventually but has not been married yet.
그러나 결혼은 필수가 아니라 선택이라고 생각하는 사람들이 증가함에 따라 미혼이라는 말 대신에 결혼을 선택하지 않는다는
의미의 비혼이라는 단어가 사용되기 시작하였다.
= however, since there are growing number of people who think that marrige is not necessary but optional and choose not to get married, the word '비혼(Bi-hon)' meaning that someone chooses not to get married, started being used instead of '미혼(Mi-hon)'.
As Hwang Sunmok said,
미 = "not done yet, incompleted"
비 = "not"
혼 = "marrige"
Therefore, 미혼 = "not married yet (because she/he is not ready yet)",
비혼 = "not married (on purpose)".
Hope you got the point. )