Due to a chromosomal quirk, female birds may have special control over the sex of their offspring. Female birds have the one Z chromosome and one W chromosome, while males have 2 Z's, which means a chick always inherits a Z from its father and either a Z or a W from its mother. For birds, the sex chromosome passed mother determines the sex of the offspring, the reverse of how it works in all mammals. (In case you're wondering, the "male" designation always goes to the sex that makes sperm, or the smaller gamete.) So by preferentially keeping eggs with either a Z or W chromosome, female birds can bias the offspring sex ratio.
When a female blue tit mates with a high-quality male, for example, she tends to have more male offspring. High-quality males can pass on their desirable traits, like good singing ability, to their sons. This becomes particularly important because a high-quality son will mate with many females, so the best way for a female to insure her own genes will spread is to hitch them to the desirable genes of a high quality male.