Muteness means not being able to speak. A person that cannot speak is called a mute. A mute keeps the ability to hear the speech of others. If not, the person would be a deaf mute.
Muteness is a type of speech disorder. A person who chooses not to speak is said to be silent rather than mute. Slang for this (British English) is "keeping mum".
Originally, the common word dumb or dumbness used to mean "unable to speak". Unfortunately this was taken over to mean "unwilling to speak" or "unintelligent". So people prefer "muteness". "Dumb" is a much commoner word, and might be used if it would not be misunderstood.