An Ambiguously Brown character is a character with a darker skin tone that clearly stands out from most of the cast, but it's not entirely clear what race they are actually meant to be. Their heritage is never mentioned, and their facial features don't correspond to any particular race either, so it's unknown. They're just brown.
Generally, this is primarily a trope in drawn media — most live-action characters are assumed to be the same race as the actor by default, although it could apply if there is some reason to wonder about this character specifically. For actors who are ethnically ambiguous, see Plays Great Ethnics. It also does not apply if the character has a defined race or ethnicity, even if that race does not exist in the real world.
This can be considered an easy way to add visual diversity to a work when the author doesn't want to deal with real world racial issues, although it could also be considered to lack real representation.
Oftentimes, this is the result of trying to avoid Monochrome Casting while having Only Six Faces — everyone looks the same except for coloring, anyway, it's just that this one has darker skin. Compounding this issue, while some features such as blue eyes or extremely tight curls are more racially distinctive, light brown skin + dark brown hair is found everywhere around the world, which can make it difficult to narrow down. Can also be the result of unusual skin and hair combinations.
Cultural differences can come into play here as well — compare Mukokuseki: in principle anime characters who are supposed to be "stateless". In older European works, where the population is predominantly white the word "dark" is often used to mean someone white, with dark hair and dark eyes. Dark skin is used in anime to stand a character out from others to deliver a 'foreign' or 'Far off' background. Often in a flair of mysteriousness or even intensity.
In anime, if a character is fully East Asian, it's often because there are East Asians who are naturally that dark and not interracial, such as Okinawans and some Koreans.
If most of the cast is various shades of brown in a future world, it may be In the Future, Humans Will Be One Race. For an even more extreme version, see Amazing Technicolor Population. If the character's skin doesn't even look like that of a human's, then it's most likely to be Ambiguously Human.
See also But Not Too Foreign, of which this is a Sub-Trope, and Mixed Ancestry Is Attractive, for when a multiracial character (who may or may not be ethnically ambiguous) is seen as attractive and intriguing.
