Everyone on the site gets their own "clipboard" if you will, we call it the scrapbook. When you roll over any block in edit mode, you can Copy to Scrapbook on it and save it to your personal scrapbook.
Later, if you're on another page and want the same block, instead of adding a new block you can choose Paste from Scrapbook and see a list of all the blocks you've saved for later.
When you add a block from your personal scrapbook you are making a new instance of that block. That means this is totally not useful if you want to have the same block show up in many placed but be editable from a single location.
In-context editing is very intuitive for most people. We tend to think of websites as a series of pages that contain stuff we want to change, so going to the page in question first makes a lot of sense. Sometimes, however, having a central administration tool to manage a pool of data that is then "placed" where it should exist on the front end makes sense. Perhaps you're creating a sidebar block that is going to show up on hundreds of pages but you want to be able to edit it from one place. Perhaps you'd like to make a pool of content to pick something from randomly, but still be able to centrally manage. Global Scrapbooks let you pull this off with ease.
Goto Dashboard > Scrapbooks and you will see a list of all the scrapbooks you have access to along with the ability to create a new one.
Make a new scrapbook and click the View link. You will see an "Add Block to Scrapbook" button that lets you add a new block of any type to this scrapbook. You can also add blocks to these global scrapbooks from the in-context editing experience the same way you would a personal scrapbook. One important difference however is that when you place a block from the global scrapbook you are placing an Alias to that block. Now you can place a block on hundreds of pages individually and go back to the global scrapbook and make one change that impacts them all.
When you copy a block to a Global Scrapbook from the in-context editing experience you will be given an option of making a new instance of the block in the scrapbook or aliasing the original.
NOTE: Because you're aliasing the original block, if you try to place the same block many times in the same page only the first one will actually stay when you save your changes. This is admittedly annoying problem if you've got a block that needs to be repeated inside the same page a lot. It's just the product of the way this feature has matured and not a brilliant plan you don't understand. Best advice, use the personal scrapbook for this type of problem where every block you make is a new instance.