The opening scene of the film, which features a stuttering young man learning, through meditative hypnosis, how to speak clearly, serves (I think) as a metaphor for Tarkovsky the artist overcoming his own internal hang-ups and boundaries, and finally beginning to speak with his own unique and clear voice.
The film is more like a poem than a drama. It is non-linear and instead of plot, it features (like poetry) a series of visual and auditory revelations. Tarkovsky's father was a poet and it seems as if the film is a kind of homage to his parents. Though his father (as the film portrays) was largely absent during Tarkovsky's childhood, the poems remain, and give crystallization to both personal and collective memory.
The film feels both deeply personal and deeply socially conscious--a kind of meditation on family, and Russian history and society. Scenes drawn loosely from Tarkovsky's own life are interspersed and overlapped with real footage of Russia's wars and various political and social upheavals, suggesting (in true Soviet fashion) that the personal and the collective are connected. In this mixing of the poetic and the documentary, The Mirror reminded me of more recent (and lesser-known) Jean-Luc Godard films like Notre Musique, which seems to draw some inspiration from this film.
Like late Godard, the film is a visual pastiche of color, black and white, literary and artistic references. It is packed (but not over-packed) with meaning. It is a beautiful film to look at, listen to, and reflect upon. Highly recommended.