I looked it up, and here is my answer:
Images (c) Wikipedia
The cere plays a part in indicating the reproductive stage of certain dimorphic birds and also has a key function in respiration. It is located at the top of the beak and looks a bit waxy in texture. The colour and shape vary from species to species. The nares (nostrils) lie within the cere. Falcons for example have round openings in the cere where you can clearly see the nares.
The nares are located within the cere and they connect to the inner beak, which is in turn connected to the respiratory system. Thus, the cere plays a crucial role in respiration and protection of the nares.
Why do budgerigars have ceres?
The ceres are there to give you keep you updated about how your budgerigar is doing. As I said before, the cere plays an important role in respiration. Like most humans, budgies breathe through their nose. When your budgie is in a bad condition, you may be able to detect it when the ceres don't look so smooth and shiny as usual.
Above: a healthy baby budgie with shiny ceres. Image (c) Northern Parrots
Below: a baby budgie with scaly mites. You can detect it when your budgie has a crusty beak and ceres. If you see this, you have to treat your budgie, otherwise it could move down to the legs and do even more damage there. Image (c) Talk Budgies
Budgerigars are dimorphic in a way that the males' ceres turn bright blue upon reaching maternity, while the females' ceres turn tan. During periods of fertility, female budgies' ceres also appear more wrinkled. Young budgies have pale pinkish ceres that are smooth and shiny.