Looking deeply into another's soul through the eyes, and them doing the same to you. It is also interpreted as undressing another with one's eyes. Also it is an euphemism for a burning passion between two.
Did you see them, Betty, they were participating in mutual staring! And you know where that leads!
A major setting in the Eastern theater of WWII, where almost-infinite Soviets were sent into battle to fend off the invading nazi forces. An entirely urban setting, it was one of the bloodiest scenarios during WWII.
Maybe this is why the Russians call WWII "The Great Patriotic War".