Demi Moore’s character is given the Navy Cross at the end of G.I. Jane.

What it is

The Navy Cross is the second-highest military decoration for valor in the U.S. Navy, and in the film it’s presented as recognition for her bravery and leadership.

In context

At the end of the story, Lt. Jordan O’Neil is accepted back into the program after the mission, and the Master Chief presents her with the Navy Cross along with a poetry book.

Quick note

So the pin/medal people usually mean is the Navy Cross.