I always assumed that Koreans wore masks for one of two reasons: to block air pollution or to prevent the spread (from or to themselves) of disease. Masks come in different materials, thicknesses, and sizes, but I just thought the choice was dependent on personal preference and fit. Ajummas (old ladies), for example, love giant masks, in combination with huge visors, which cover their entire faces, because they're crazy, and they do what they want.
According to my co-teacher, who wears masks all the time, different masks serve different purposes.
She has one that she says "keeps her wet." (I know, I chuckled too.) She wears it to moisten her throat at night or when it's sore. It's made of thick cotton.
She has another, more industrial-looking mask, to protect from dust and some air pollution. It can be molded to her face to prevent air gaps. It also matches yellow bracelets.
Regretfully, she forgot her large, two-piece mask today. We have a teachers' field trip planned, to visit a nearby mountain for an afternoon hike. She would have worn it, had she remembered to bring it. It's a UV mask, to protect from sunburn.
It is also great at elephant costume parties.