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?
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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:
Both “writer at large” and “editor at large” are titles for people who work at magazines and/or newspapers, and the “at large” portion of those titles generally means that those people do not belong to a specific department within the magazine or newspaper. Instead, people with those titles tend to write or edit different stories – not stories that belong to a specific department (like Sports or Technology). People with these titles tend to be more talented and valued, which is why they are allowed more flexibility in their jobs.
An editor-at-large is a journalist who contributes content to a publication.
Unlike an editor who works on a publication from day-to-day and is hands on, an editor-at-large will contribute content on a regular or semi-regular basis and will have less of a say on a specific field such as layout, pictures or the publication’s direction.
However, unlike a writer, they are allowed their own preferences in the content they have to generate and don’t always have to pitch their ideas to the main editor.
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:
John Powers is the pop culture and critic-at-large on NPR's Fresh Air with Terry Gross. He previously served for six years as the film critic.
Powers covers film and politics for Vogue and Vogue.com. His work has appeared in numerous publications, including Harper's BAZAAR, The Nation, Gourmet, The Washington Post, The New York Times and L.A. Weekly, where he spent twelve years as a critic and columnist.
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.