A show bird (also known as an exhibition budgerigar or English Budgerigar) is a bird that has been bred to 'show' or be judged in budgerigar shows.
It is not just a bird that is bred and placed in a show cage for a judge to see. To qualify as a 'show bird' it must want to show. Budgerigars have the ability to throw the feathers on their forehead (frontal feathers) forward and up. This is called the "blow". This is part of showing. Much like a Peacock that shows off his tail to a Peahen. The shape and stance is also very much on show. When a budgerigar 'shows' it really does look like it has attitude.
A breeder who wishes to show their birds will put their best budgies into show cages to train them and it is from this training that a breeder will decide which of his birds will join his 'show team'.