Timidity is the noun for being timid: the state of having no courage or confidence, or an occasion when someone shows it. It is a more formal word than the adjective, and you meet it far more often in writing than in speech — in book reviews, editorials, and reports. Two uses cover almost everything. First, about a person's nature: 'his natural timidity', 'she overcame her timidity'. Second, and very commonly, about a decision or an organisation that was not bold enough: 'the timidity of the government's response', 'artistic timidity'. That second use is a criticism, and a fairly sharp one dressed in polite clothes — the writer is saying somebody knew what to do and did not dare. It is uncountable, so no 'a timidity' and no plural. The words that go with it are worth learning as a set: you overcome, conquer, or shed your timidity; you criticise or accuse someone of timidity; something is done with timidity. In everyday conversation, people are more likely to say 'shyness' about a person, or 'playing it safe' about a decision — timidity is the word you write, not the word you chat with.