Mirrors are considered unnecessary and most people do not have one.
In Jonas’s community, everyone looks alike and everyone dresses alike. Sameness is a high priority in the community. Jonas is unique in that he has special light colored eyes, that are somehow a different shade than most other people in the community. When he sees the newchild Gabe, whose eyes are also light, he remembers that people have sometimes commented on his eyes, but he never really sees them himself, because he never looks at his reflection in a mirror.
Mirrors were rare in the community; they weren't forbidden, but there was no real need of them, and Jonas had simply never bothered to look at himself very often even when he found himself in a location where a mirror existed. (Ch. 3)
You would not need a mirror if you wore the same clothes every day, and they were the same as everyone else's. Also, everyone’s hair is the same and meticulously maintained. All decisions are made by others. In fact, one of the reasons for having a mirror is to promote individuality. People look at and reflect on themselves in the mirror. You can see why the community would not want to promote that.
Jonas accepts the fact that there are no mirrors, but it is another subtle message that everyone is the same. You do not deserve individuality, the community is saying, so you do not need a mirror. When Jonas begins to see color, he comments that it would be nice to choose different colored clothes.
"Well ... "Jonas had to stop and think it through. "If everything's the same, then there aren't any choices! I want to wake up in the morning and decide things! A blue tunic, or a red one?"
He looked down at himself, at the colorless fabric of his clothing. "But it's all the same, always." (Ch. 13)
He tells The Giver that it doesn’t really matter what you wear, because clothes are not important, but in actuality, as The Giver points out, "It's the choosing that's important…” (Ch. 13). In eliminating colors, the community has removed the ability to express individuality. It is another way to keep people from being different.
A lack of mirrors is just one minor way that the community keeps control of its members. They have subtly eliminated any way that people might distinguish themselves from others, except for the necessary ones like names (even though people also have numbers). Being a part of the community and a contributor to the group is more important than being an individual, and people are reminded of that daily- from getting dressed.