This is called courtship. Courtship displays, especially those of birds, can be elaborate and spectacular. Great crested grebes perform a dramatic dance in the water, in which male and female present water plants to each other. There are other ways to attract mates besides singing and dancing. Many male animals are brighty coloured.
Some animals attract mates with scent.
Female gypsy moths have a scent that a male can smell 11km away. Male monitor lizards have harmless wrestling matches to win a female. Owls can hear sounds ten times softer than any human can hear. The Arctic fox turns white in winter to camouflage itself against the snow. Flatfish can change their colour and marks to match the seabed in seconds.