There is no viewable clipboard on an iPhone at all. Items saved to the clipboard will be able to be pasted again and again until you overwrite them with the next thing you copy to the clipboard. On a Mac, you can choose 'Show Clipboard' from the Edit menu in Finder. You don't have that option on an iDevice.
On both a Mac and an iPhone or iPad, you can only store one copied item on the clipboard. This one item can only be pasted as the whole item, so if you copy a page of text, you can only paste that page of text, not certain parts of it.