When you sing unaccompanied, you pull sound out of thin air with nothing but your lungs and your throat. You find a key and you sing around the overtones. You can help make harmonies that are not forced into whatever an instrument's (or an instrumentalist's) limitations are.
Solo unaccompanied singing by a traditional singer can be a complex thing. I think it was my landlord Stephen Parker who referred to this as "horizontal harmony". I know there are actual classical-music terms for the sorts of ornamentation and note-bending that this describes, but horizontal harmony works best for me.
I was thinking about this for the oddest reason the other day. It seems to be an occasional practice in commercial arranged marketable music for a recording to begin with a little bit of unaccompanied singing before some accompaniment comes in. I have always been drawn to those few beautiful moments, myself. I was watching what may be the worst Doris Day film ever (Move Over, Darling),which included a scene where she sings a song to her children. It begins unaccompanied, and Doris Day (despite everything surrounding her persona and cultural position) is a wonderful singer, with amazing intonation. I was transfixed at the singing. Then a sappy accompaniment swelled up. It wasn't even overpowering, but it destroyed the brilliance for me.
Many years ago, accompanying my parents to various folkie events and music parties, I would often find myself in situations where people were exchanging songs. On occasion there would be people with guitars who seem to have been infected with the disease of a belief that singing is always better with instrumental accompaniment, and they would, unasked, start to play along. I was too young at the time to express my dismay, even when this was done to me (although I knew immediately that there was something wrong about this, as the chords -- and sometimes even the rhythm -- I was hearing in my head were rarely what was being played), but I did have the wonderful experience once of watching somebody reach over and put her hands around the neck of the offending guitar, stopping the sound.
It's been years and years since I've found myself in such a situation, and certainly the folks I sing with these days love and appreciate the unaccompanied at least as much as I do. But not long ago I was at a large party of different social groups where there was singing up on the third floor. I sang something at one point when somebody tried this unasked-for accompaniment rudeness. But I'm not a kid among the adults now and I know what I'm doing. So I just modulated up a few cents, perhaps a quarter tone, solid and strong and unwaveringly immediate in the transition, which absolutely baffled the player who looked as his guitar as if it had betrayed him. I'm not entirely sure he knew what happened but he did give up, without me saying a word or even acknowledging him.
I considered it a triumph, if a private one.