The phrase symbolizes the truth that's overlooked because of appearance, deception, or willful ignorance. When Jill pointed out the discrepancies in the budget, it was like the emperor had no clothes.
Pro Tip 2/3
Cultural Insight
It's from a fairy tale where a child exposes the truth that the emperor is swindled and actually naked. You stating the project will fail when everyone is praising it is like saying the emperor has no clothes.
Pro Tip 3/3
Risk of Offense
Using the phrase can imply criticism of conformity or expose someone's delusion, possibly offending others. Henry took a risk saying the emperor has no clothes during the board meeting, but he was right.