The icon of the Smolensk Mother of God is an example of a hodegetria: an icon depicting the Virgin Mary holding the infant Christ. Tradition has it that the icon was painted by St Luke himself. It passed from Antioch to Jerusalem to Constantinople, and then on to Russia, where it eventually ended up in Smolensk in the eleventh century. Various miraculous events were attributed to the icon over the years, and copies of the icon also took on its powers. Kutuzov, here, is wielding one such copy.
The original icon is believed to have been destroyed by fire during the German occupation of Smolensk in 1941.
Examples of Russian icons can be found illustrating many of War and Peace's bookmarks. In the Russian Church, icons were far more than decorative images meant to illustrate moments from the Bible: they were a direct link to the world of the divine. Strict rules of composition and style of icon painting was handed down from the church in Byzantium; they are seen as the Holy Gospel in paint, and are venerated as such. See here (about three quarters of the way down the page) for more on the significance of icons in Russian Orthodoxy.