In this NPR news excerpt, it says:
But first let's turn to our critic-at-large, John Powers, who says seeing "Godzilla" again has made him nostalgic for old monster movies.
What does critic-at-large mean?
The phrase at large has the general meaning free, unconstrained.† We say, for instance, that prisoners are ‘at large’, meaning that they have escaped and have not been recaptured; or that a dog is allowed to roam ‘at large’, meaning it not is not confined by a fence or a leash.
This use is extended to the figurative sense of ‘general, not constrained to the particular’. Specifically, it was not unusual in the 18th and 19th centuries for one of the states of the United States to provide for two sorts of member in their legislatures: some members elected by specific communities, and other members elected by the entire state. The latter, since they did not represent particular constituencies were designated ‘members at large’ or ‘members-at-large’. (Today this is fairly rare in US governments; but you will still find it in professional and social associations.)
In the late 19th century we find that an independent newspaper, which was not bound to the policy of any particular party, was occasionally described as a ‘critic at large’ of society and politics. But the modern use arose around WWI when many newspaper and magazines had ‘critics at large’, reviewers whose ‘beats’ extended beyond a particular art. Mr. Powers plays that role at NPR. He is not a film critic or a music critic or a theatre critic or a literary critic but a critic of ‘things in general’—a critic-at-large. He is unconstrained: he can write about anything he likes.
† At large is also used in a quite different sense: ‘extensively, at length’. Mr. Knox has written at large upon this matter.
The phrase at-large (when appended to a position title, such as member-at-large or editor-at-large), is used to describe someone who is a distinguished yet peripheral member of a board or staff. As one website explains:
Since NPR considers Powers a critic-at-large, my initial guess (after reading your question) was that John Powers writes as a critic for a number of prominent publications, and is also a regular contributor at NPR. Sure enough, his biography reveals:
I would say that at-large functions similarly to the title emeritus (as in professor emeritus), except that emeritus is used for individuals who are semi-retired yet still contributing in some capacity, while at-large is often used for people who are currently active rather than retired. Both tend to be honorific designations.