Translation:The girls are looking into a mirror.
Why is "The girls look at a mirror?" not correct?
Because that would indicate that they look at the mirror itself ("Die Mädchen sehen (sich) einen Spiegel an").
However, "in einen Spiegel sehen" implies looking not at the surface of the mirror (in order to see the mirror) but to look at the reflection which the mirror shows -- they want to see (for example) themselves. That is, they want to look "into the mirror".