It is said that the eyes are the windows of the soul. In this case, the left eye is the window, while the right eye is a painted on window. This means that the left eye shows emotion and feelings, while the right eye shows what you want others to see.
This idea is rooted in biology. The left side of the body, including the eye, reflects the right hemisphere of the brain, which contains your sensations and emotions. The left hemisphere contains your intellect. Therefore, if you are observing someone, look at their left eye to see what they are really feeling. If their left eye looks gloomy, while the right looks cheerful then they are trying to conceal their true emotions.