The Gemara says in the third perek of Mo’ed Katan that you’re not allowed to take a haircut or shave on Chol HaMoed unless there’s an oneis d’muchach – an (unavoidable incident) that everybody in the neighborhood was aware of that prevented you from doing so on Erev Yom Tov.
So let’s say I was sitting in prison and they released me on Chol HaMoed, or I was in the hospital and there were no barbershops in the hospital. Everybody in the neighborhood knows I didn’t have an opportunity to take a haircut on Erev Yom Tov, so I’m allowed to take a haircut on Chol HaMoed.
If someone shaves every day and shaved on Erev Yom Tov, Rav Moshe Feinstein writes that he can shave on Chol HaMoed because he came to shul and everybody saw he was clean-shaven. It’s an oneis d’muchach that everybody knows about since he couldn’t shave hair that didn’t grow yet and there was nothing he could do to prevent himself from needing a shave on Chol HaMoed. So Rav Moshe says it’s muttar, strictly speaking, but since so many people don’t shave on Chol HaMoed, it’s better not to, he said.
Rav Soloveitchik used the same reasoning as Rav Moshe – that it’s an oneis d’muchach – but he added that since it’s permissible to shave on Chol HaMoed, you have to shave in order to look good. The statement “Hameveze es hamo’ados, ein lo chelek l’olam haba [One who demeans the holidays has no portion in the world to Come]” refers to Chol HaMoed. You have to dress Yom Tovdik on Chol HaMoed. You have to look good.