A coo is the low, sweet sound that a bird makes, especially a dove or pigeon. If a dove builds a nest outside your open window, you'll be able to hear its coos every morning.
There is a small, gray pigeon that's called a mourning dove because its coo is so sad sounding. When you hear a bird making this distinctive sound, you can also say that it coos — and if a person murmurs in a low, soft voice, you can say that she coos too. The word coo has been used since at least the late 1600s, and its origin is probably imitative, the word sounding very much like the sound it describes.