Think of it like someone trying to stand out from the crowd in a way that's a bit over-the-top.
Here are some examples:
* She ostentatiously displayed her expensive jewelry.
* He wore a bright red suit ostentatiously, hoping to be noticed.
* The new CEO arrived in a limousine, ostentatiously making his entrance.
Essentially, it's about doing something in a way that screams, "Look at me!"