A reserved person does not easily show feelings or talk about what is wrong. They keep a lot inside. They may be polite and calm, but they do not open up quickly, and they may not like big talk about private things. This is about character, not about being unkind. Though actually, reserved is not the same as shy. A shy person is often afraid of people; a reserved person may simply choose not to share. Older, careful English likes this word. In everyday talk, quiet or private are close, but reserved points more to holding feelings back. The same spelling has another, very common use: a reserved seat or a reserved table is kept for someone. That second use is about booking, not about personality — same shape of idea (kept back), different job in the sentence.