Most female birds incubate the eggs while the male defends the territory from other males. Singing would only draw the location of the nest to the attention of predators. By being silent the female protects herself and her young from danger. The songs of the male attract a potential mate. They advertise also that the territory is taken and other males must keep away.
Songs help to maintain the bond between the male and female.
It reassures the female that the male has not left. This reduces the chance that she will leave the nest to mate with another male that may be singing nearby. The male selects song posts from which it sings. By singing regularly from each of its song posts the male defines its territory. This lets other males of the same species know that the area is taken.