The character-set panel displays a portion of the currently selected font. Unlike the Character-set overview, which you call up with the [Control]+[Esc] keys, the characters shown here appear as they are defined in the font. Since there is room for only 12 characters in the display field, use the scroll bar or the arrows at the left margin to move through the list.
When this overview is visible in the function panel, a click of the mouse on one of these characters will make it appear at the cursor in the text frame or text editor, as if you had entered it from the keyboard.