A warrant canary is a colloquial term for a regularly published statement that a service provider has not received legal process that it would be prohibited from saying it had received. Once a service provider does receive legal process, the speech prohibition goes into place, and the canary statement is removed. Source
In a nutshell, a “service provider” hoists a flag periodically that affirms they have not been subpoenaed for user information by a government agency. Often times these national security letters come with a gag order to not discuss the request. By not updating the warrant canary, or the canary disappearing, a provider can passively inform their users that an agency may have requested information and they’re now under a gag order. It’s a cute, and believed-to-be-legal way to inform users that their information may no longer be safe with the provider.
Canary Watch has even gone further and keeps an eye on any warrant canaries that are out there! Service providers watched on the site include reddit, tumblr, Adobe, and Cloudflare, among many others.