Songs are involved with courtship and mating and are therefore heard mostly during the mating season. It is almost always the male who sings. Females sing rarely.
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.