Ignoring other prominent thematic fields like family or marital problems and Russian or Soviet history (from Pushkin via Stalin to the current fear of a Chinese threat), two topics can be extracted from the movie which Tarkovsky seems to be very concerned about: 1.The confrontation of Man and Nature as two opposing powers, and 2.The continuum of time (the equation of present, future and past).
The importance of topic 2 can be made clear by just considering the film's structure: The different time levels are intertwined in an often deliberately confusing way so that it actually becomes difficult to identify them. The fact that the same actors are used to portray different characters of different time levels (Maria=Alexei's mother and Natalya=Alexei's wife; Alexei as a child and Ignat=Alexei's son) underlines the idea of deliberateness in addition. But the interconnection of times is also made visible by the recurrent theme of the so called 'déjà-vu-phenomenon': A character perceives a new situation or action as if it has already occurred before. In fact, he or she gets a notion of the predetermination of everything that happens in his or her life - a horrid thought, because then you can't change anything and have to accept willingly whatever an obscure determinating force has planned for you.
Let's concentrate on the last sequences in which the significance and the combination of these themes become obvious. First there is the scene where Alexei, who lives in separation from Natalya, lies in agony, overcome by an unknown disease. He just has the energy to make a last statement for posterity ("I simply wanted to be happy!"), then he retires from the world, asking to be left in peace.
But while he is on the brink of death, he still succeeds in wondrously stirring up life. He takes into his hand a moribund bird, which is lying on his bedside table, squeezes it, and then lets it go so that it can fly up into freedom.
Is it the same bird that breaks through a window glass in another scene, or that places itself on the head of that orphan boy whose parents have perished in the Leningrad blockade, as if he wanted to protect him?
The birds of "Zerkalo" seem to take up a symbolic function similar to the dogs in other Tarkovsky movies (i.e.: "Nostalghia", "Solyaris"): They represent some kind of link between Man and Nature; they are frontier guards at the gates of the unknown.
Tarkovsky sees Man and Nature as two opposing, incompatible powers. This becomes evident again and again, for instance when a vigorous wind repeatedly runs through grass and trees or when drumming rain drenches the landscape. Here Man can only watch in amazement, being unable to set something of equal value against the inscrutable elemental forces.
In the closing sequence Man appears at first as if he was embedded in the womb of Nature. Maria, the future mother of Alexei, is lying dreamily in the grass when she is asked by her husband whether she prefers a boy or a girl. But instead of answering his question she is gazing into the distance, and suddenly she sees herself as grandmother, walking across woods and meadows having little Alexei (Ignat?) and his sister by the hand. Then a juvenile Maria appears again, and tears are running along her cheek, but she is smiling at the same time. It seems as if the knowledge of the unstoppable progression of human existence into a single direction (towards old age and death) makes her sad and happy at the same time. She feels grief because of the inevitable loss of youth, but she also rejoices in happy relaxation for she has made out the rules of life as such and has accepted them.
At the end the camera follows the way of the grandmother and her grandchildren for quite a while. But again and again trees interfere and obstruct the view on the humans like gloomy barricades. Until finally both ways separate irredeemably: The humans have disappeared somewhere in the distance whereas the camera shot pans into the dark impenetrability of the forest.