"Giving details" is a little too general to cover this definition. "Obscure trivia" usually means something like "information related to the topic that not too many people know and/or find useful, but is still interesting nonetheless."
For example, an obscure trivia fact about Philadelphia could be that the colors of the city's flag reflect its historical connection to Sweden since it was built on land that was once a short-lived Swedish colony. Is this a fact that many people don't know? Yes. Is it useful? Depends on how you look at it. Is it interesting? Sure, if you enjoy learning about these types of connections.