Budgies have got their eyes on the side of their heads, which provides them a wide visual field, useful for detecting predators. Birds that have eyes on the front of their heads, such as owls and eagles, have binocular vision, which is in turn useful for estimating distances while for example hunting.
Images © Wikipedia
While humans have only two eyelids, budgerigars have a third concealed eyelid that is called the nictitating membrane. This thin and transparent "eyelid" sweeps across the eye like a windscreen wiper, acting as a lubricating duct - equivalent to our tear duct. The nictitating membrane also covers the eye and acts as a kind of contact lens in many aquatic birds when they dive underwater. When your budgie is asleep, the lower eyelid rises to cover the eye completely.
If you look hard enough, you will be able to see the nictitating membrane on the picture below. It's quite hard to see in general, as your budgie often moves it with lightning speed. I have seen it in one of my budgies, Wit Zingbeest. Back then, I didn't know why he suddenly covered his eye with a transparent layer. I thought he was tired of me talking to him, but still showing his eye somehow to indicate that he was listening :-)
|Image © Birds Online|