When you choose to paste a selection as an object, you are pasting not only the data, but information about which application created the data (the 'source application'). That means that you can use all of the power of the source application to create content, format, and manage the object.
An embedded object is an object that is created and managed by an external application. Instead of saving its document as a separate file, the document is saved ('embedded') within the parent, or host application. It is shown as an object in the document of the host application.
The host application can typically manage the position, size, and basic formatting of the object itself. To make substantive changes to the content or formatting of the object, you have to use tools from the external application, which typically involve activating the object (by double-clicking it) or turning on a toolbar.