Tarkovsky's films seem to exist in a different type of time orthogonal to our own, and the experience of engaging with them is difficult to describe. They are both powerful and ineffable.
From his writings, he could be mistaken for a practitioner of Zen. I would like to share my favorite Tarkovsky quote:
"Everybody asks me what things mean in my films. This is terrible! An artist doesn't have to answer for his meanings. I don't think so deeply about my work - I don't know what my symbols may represent. What matters to me is that they arouse feelings, any feelings you like, based on whatever your inner response might be. If you look for a meaning, you'll miss everything that happens. Thinking during a film interferes with your experience of it. Take a watch into pieces, it doesn't work. Similarly with a work of art, there's no way it can be analyzed without destroying it."