Cleopatra is a great example of making grand entrances haha..
Is your source referring to when she met Mark Antony? Her "grand entrance" was that she came sailing on a huge boat with lots of flower, servants and fancy clothes and she used a LOT of perfume so that Mark would smell her before seeing her :p
So, when you make a grand entrance, you enter a place or introduce yourself in a way that totally captivates people or draws their attention. Stylish entrance, indeed :D