Content-Language: the audience a document is for

The distinction from the lang attribute is real, not pedantic. The attribute tells a screen reader or a spell checker which language a particular run of text is in. This header tells a recipient who the document is meant for, which is why a Maori language primer written for English speakers can legitimately declare en even though most of the words on the page are not English.

Multiple tags mean a document addressed to several audiences at once, such as a bilingual notice, rather than a set of alternatives to choose from. If you have separate translations at separate URLs, each one declares its own single tag, and the relationships between them are expressed with link relations rather than by listing every language here.

It is the response side counterpart of Accept-Language. A negotiated page should state which language it settled on, so a cache and the client can both see that this body is the French variant rather than assuming it matched the request. Without it, a debugging session over a wrong language page has nothing to inspect.

It applies to any representation, not only HTML. A PDF, a plain text file or a generated image with a caption can all declare a language, and for anything that has no internal way to say so, the header is the only signal a client gets.