The default SharePoint interface is a little bit time consuming for heavy users, for example I must make at least 5 clicks to add a new folder, the same amount for uploading a document and login two times if I want to edit a document. (and don't forget all the work you must do when adding a new blogpost with pictures... I use Windows Live Writer ;-)
When you use Groove's functionality to synchronize workspaces with SharePoint libraries, you only have to: Right click "add folder", right click "add document", "double click open document"... and after you are finished editing, adding, etc... just click synchronize and your done. Works almost the same as your Windows Explorer..!
And with Groove beside [in tandem with] SharePoint you can work offline and give others, who are not in your companies directory, access to the files.
from Groove and SharePoint differ, but also work together:
Using Office Groove and Office SharePoint Server together
In some cases, your best course is to use Office Groove and Office SharePoint Server in tandem rather than either one alone. "They're not mutually exclusive at all," says Bob Barnes, a senior specialist at Conchango plc, a Microsoft Gold Certified solution provider headquartered in London. For example, Office Groove lets you import Office SharePoint Server document libraries into your workspaces. Thereafter, if someone adds or edits a file in Office SharePoint Server, it appears in Office Groove, and vice versa. Thus, team members can use Office Groove as a tool for taking Office SharePoint Server files offline, or as a simple way to give vendors and partners access to Office SharePoint Server content on your company's intranet.
You can use that same functionality to link field teams with the head office. An insurance company can create an Office SharePoint Server document library for its claims inspectors at headquarters, for example, and include it in an Office Groove workspace that its mobile claims adjustors use. As adjustors complete claim forms on their laptops during the day, they can store them in Office Groove. As soon as they reconnect with the Internet, Office Groove automatically uploads those forms to Office SharePoint Server for later review by managers at headquarters.
This is a Dutch post from Bart Wessels about this with some more details