Mirrors used to be the number one essential toy for pet parakeets, but not everyone agrees that they are actually good for the bird's mental health. If there are two or more birds in the cage, the mirror is simply a bit of fun, and will not impact their socializing or behavior.
For a single bird, a mirror may become an object of obsession. The parakeet will think the reflection is another bird, and may direct all its social needs to the reflection. This can slow down hand-taming in single birds, and can also lead to frustration, as, clearly, the mirror image is not going to chatter and interact as much as the real parakeet would like!
Parakeets and mirrors - something to reflect on
Are Parakeet Mirrors Bad?
Some countries, since the 1980s, have actively discouraged the sale of pet bird mirrors - Germany, for example, where parakeets enjoy huge popularity in the pet trade. The argument is that the lack of feedback from the reflected bird in the mirror will slowly drive the poor parakeet mad.
And yet, many parakeet owners report nothing but harmless fun from the interaction of bird and mirror. The birds are very intelligent, and although they are not able to work out that the reflection isn't actually a second parakeet, they are still able to interact with their owners, become hand-tamed, and (sometimes) learn to talk.
So, mirrors are not bad; but keep an eye on a bird who becomes a bit obsessed (watch out for repetitive actions such as shuffling along the perch, tapping the mirror, shuffling back, and repeating the sequence endlessly, or squawking at the reflection with head feathers bristling - both signs of frustration). In these circumstances, consider getting a second bird - once there is more than one parakeet in the cage, the mirror is no longer an issue.