There are many contributing factors that make a good wildlife image a great one. The light, the subject, the background and for me one of the most important factors are the eyes.
Often when filtering through a particular scene or sighting you will immediately notice that the images that have your subject's eyes open are a lot more attractive than when the eyes are closed or about to close. When your subjects eyes are open and has natural light falling on to it, this enhances the feel even more.
Some subject's eyes can be extremely difficult to capture, purely because their eyes seem to be situated further back and often have a lot of darkness around it to be able to absorb the light coming into the eyes. Most of the diurnal hunters such as African Wild Dogs and Cheetahs are prime examples, where the dark areas around the eyes are designed to absorb the harsh light, allowing them to look into the sun whilst focussing on prey species. For these animals the best time to get light into the eyes is during sunrise and sunset when the sun is on the horizon.
A perfectly positioned Cheetah, except for the fact that there is no light in the eyes
Notice how the light in the eyes makes all the difference
During late morning of early afternoon when the light is quite harsh, it is virtually almost impossible to get any shine in their eyes.
Lions and Leopard who are generally more nocturnal hunters tend to have lighter colours around the eyes, often making it a little easier to get that beautiful glint in the eyes. As for most of the species, the best time to get light into the eyes are during the early morning and late afternoon hours.
So next time when you are out in the field, pay special attention to your subject's eyes and carefully position yourself so that you have the light hitting your subjects eyes.