How did I make this screen appear?
It sounds like you probably activated the "Application Windows" feature of Mission Control (previously Exposé) in an app that didn't have any windows open.

It looks like this if you have no windows in that app open:


The list of files are recently opened files in that application (in this case, TextEdit).

How you opened it depends on your particular setup. You can set a keyboard shortcut for it in System Preferences under Mission Control, but I think there are also gestures. I don't have a Magic Mouse or Trackpad with gesture support handy, so I can't confirm exactly what may have activated it for you. Look through the Mouse panel in System Preferences for any reference to Exposé or "Show Application Windows" or similar for an idea of what exactly activated it.