An allowlist (or allow list) is a list of individuals or domains who are expressly permitted by the site using it. The opposite is a blocklist, where anyone on the list is specifically not permitted.
Other terms for this may be safe list, permit list, accept list, etc. The legacy term "whitelist" is discouraged.
In the context of moderation, this would be individuals who would be allowed to have their comments displayed bypassing other moderation types.
This is useful in avoiding the burden of having to moderate for known/trusted individuals and to only have additional levels of scrutiny for newer individuals.
WordPress, for example, has a feature where it will automatically approve any comment by an individual with a previously approved comment. This is the simplest way to generate such a list...people you trusted to comment in the past may comment in the future.
David Shanske added a textarea to the WordPress webmention plugin that contains a list of domains allowed to bypass moderation. For moderated webmentions, there is an option to allow, or allow all webmentions from that domain.
gRegor Morrill: my ProcessWire Webmention plugin has an allowlist of domains it will accept vouches from. The plugin supports monitoring a blogroll and adding new links it finds as well as manually updating the list of allowed domains.
This is working on gregorlove.com since 2016-04-10. The list is only used if the option "Require webmention with Vouch" is enabled. Since Vouch is not widely implemented, I do not have this option on currently.
As noted in a discussion on Responses at IWC Berlin 2018, a list like this may not mean display or not display...it may mean a reduction in the amount of detail displayed.