If someone looks peaky, they look pale and a bit unwell — the face has lost its colour, the person seems tired or washed out, as if they are coming down with something or have not eaten properly. It is a gentle, homely, informal word, the kind an older relative uses: 'You're looking a bit peaky, love — sit down, I'll make you some soup.' Three things to notice about how it is really used. First, it is far commoner in British and Irish English than American; many Americans know it but would say 'pale' or 'washed out'. Second, it is nearly always softened — 'a bit peaky', 'a little peaky' — because it is a kind remark, not a diagnosis, and saying someone is 'very peaky' sounds odd. Third, it goes with looking or seeming: 'you look peaky', 'he seemed peaky', rather than 'I am peaky'. It describes how you appear to someone else. It also leans older; younger speakers use it less, so hearing it often marks the speaker's generation or a warm, family setting. And it is mild — a peaky person is off-colour, not seriously ill.