Question: Somehow I have gotten my Mac Mini into a state where every time I press a modifier key - shift, option, command or control - it shows an image of the symbol of the modifier key around the upper right of the screen. This is quite annoying and I do not know what this feature is called so it is difficult for me to find information about it. How can I disable this "feature"?

Answer: 
It sounds like you have the “Sticky Keys” feature enabled.

To control the setting, open the *System Preferences* application ( > System Preferences…), load the *Universal Access* preference pane, goto the *Keyboard* tab. You can turn “Sticky Keys” Off (or On) there. You may also want to disable the “Press the Shift key five times to turn Sticky Keys on or off” feature. Or, if you want the sticky feature without the display, just disable “Display pressed keys on screen” and leave it enabled.
Go to System Preferences then select "Accessibility" then in both "General" and "Keyboard" sections, disable the sticky keys in the Keyboard and de-select the Sticky Keys in the Keyboard section.