Tradition has is that Nero played a fiddle while Rome burned.

This story is highly speculative.

A fiddle is another name for a violin.

Rome.

But Nero was not playing a fiddle, that is a complete myth.

The fiddle wasn't invented for another 1,500 years.

According to legend, Nero, although the more famous version states that he played the fiddle while Rome burned (although the fiddle hadn't been invented yet).

It means to do something trivial or meaningless while there are more important things that need taken care of. Can you imagine there being a great fire and someone just ignoring it and pulling out a violin and playing as if nothing is happening?