The Mirror has autobiographical elements but no discernible plot. For those of us who didn't understand the presence of the balloon in Andrei Rublev, there's a balloon in this one, too (starting at about 39 minutes), so maybe he just liked balloons.
You can watch it at Youtube, but embedding is disabled.
Senses of Cinema says,
questions of the film’s alleged impenetrability dissolve under the impact of moment after moment of the most visually stunning, rhythmically captivating filmmaking imaginable.FilmRef.com says,
If ever a film embodied the concept of cinema as a recreation of the human thought process, Mirror is it. Not only is it Tarkovsky’s masterpiece, but it is one of the high points in the development of modern cinema.
To attempt to conform these images into some coherent plot or universal conclusion is meaningless. After all, Mirror is a reflection of Tarkovsky's haunted soulThe Arts & Faith film list says,
the sheer visual power of the images in The Mirror exerts a strong spiritual impression, even if their meaning is not readily apparent. Additionally, when the viewer accepts Tarkovsky’s approach and interacts with the film on his terms, it can evolve into a profound meditation on memory, love, sacrifice, and rebirth.The book 1001 Movies You Must See Before You Die calls it "a beguiling and remarkable film". It gets a score of 100% at Rotten Tomatoes.