Kittens meow to their mothers to request something. When they grow up and become adults they do not meow to each other anymore! Scientists believe that the reason adult cats meow is an extension of their baby behavior and that the cat is trying to communicate a need to it's owner!
Adult cats use many other methods to communicate. They use hissing, purring and growling with their vocal cords. However, a lot of their communication is with body language; for example, they arch their backs to signify fear or aggression. The positioning of their tail usually expresses their level of happiness: the higher up it's held, the happier the cat is. Finally, cats also use scent to communicate! They pee on their territory and they rub off against people and objects to imprint their scent onto them to communicate to other cats that those things are theirs!