My Samsung Galaxy S III claims that a screenshot was "copied to clipboard". What?
The clipboard (like on Windows for instance) can hold different types of data.  

Raw images (like your screenshot) are one of those possible clipboard contents and thus you can paste them in, given that the app you use allows you to paste image data from your clipboard.

The supported data types that the clipboard can hold are mentioned in the Android Documentation (https://developer.android.com/reference/android/content/ClipDescription.html).
I believe it either saves an Intent with the type ACTION_ATTACH_DATA or a Uri to your image or holding your image as a data string (Base64 encoded).