^^^ But since human hearing is not flat, a flat response could yield all kinds of lows and highs a particular listener does not want.
To answer OP’s question, I think of detail as the ability to hear distinct sounds in the program material. Like when I upgraded my audio interface to film capacitors in the analog stages, and suddenly I could hear sounds I didn’t know existed. I could hear the timbre of a wood-bodied instrument, such as a cello. I could hear the ugly sound of guitar strings rattling against one of the forward frets, even though I was pleased to actually be able to hear such a detail. It is in fact a caveat to have a detailed (read that: revealing) system because it shows you when a recording is truly bad.
I don't see why a bright system is associated with detail. It's a different phenomenon in my opinion. I think Sennheiser HD's of various models are bright sounding, but this doesn't give them any increased ability to be detailed. I'd say the equipment behind is has greater affect on detail.