There's a great book on mirrors that I need to recommend: In the Looking Glass: Mirrors & Identity in Early America by Rebecca K. Shrum. To start with this question, there isn't a clear "not knowing" of how people looked. Shiny objects and water offered reflections that gave people a general sense of their appearance, albeit distorted. Really, the change mirrors brought was the ability for people to accurately see themselves instead of a distorted image. The way you look in a spoon or a pond looks incredibly different from a mirror. The technology to make mirrors began in the European Renaissance, however it was over the seventeenth and eighteenth centuries that they became commonplace. Early mirrors might mean a couple of things like looking glasses (glass blown in with a spherical bend) or small metal pieces, which were often used for trade in the early colonization of North America.
Schrum cites research that found mirror ownership by the English middling class nearly doubled between 1675 and 1725. Similar growth occurred on both sides of the Atlantic. Mirrors also served to illuminate homes, so in the eighteenth and nineteenth centuries as they became common, more mirrors where built with candleholders attached.
As for impact, Shrum discusses how a number of groups experienced mirrors and accurate reflections. These were somewhat luxury goods, especially depending on the quality. In WPA interviews taken in the 1930s, formerly enslaved people referred to mirrors, often linking them to freedom. In one example, Millie Manuel described her home during enslavement, "We had timber rail house. No beds in it. We slep' on the floor on a pallet. We didn't have no chair and we didn't have no mirror...I didn't knowd what I looked like 'til I was free." Imagination of a person's appearance was tied to freedom.
Europeans traded mirrors with Native Americans as a common good that crossed cultural lines. Most European mirrors came in a case or frame. However, Indigenous people often removed the casing to put in their own holders or even sew onto clothing. It was so common that they sometimes requested mirrors to take the glass for their own modifications.
Mirrors also gave nineteenth century women the opportunity to define their public image. Whereas their public self was determined by men who looked at them, mirrors gave women the chance to look at themselves. Some women even trusted mirrors more than their friends when determining their appearance. That reforms an idea of societal power where previously others needed to confirm or advise, people could reclaim that authority in curating their selves.
Again, I strongly recommend Shrum's book which goes into further detail on all these ideas, especially the relationship between whiteness and mirrors. I did my best to summarize the main arguments here, but I'll finish with a direct quote from the conclusion that captures the core thesis:
Mirrors, as we have seen, also offered people extended opportunities to engage with an accurate image of themselves and to construct a self-identity that relied at least partially on that image, a quintessentially modern practice. Men and women of African, Native, and European descent embraced the mirror's ability to make self-knowledge available to them (Shrum, 160).