Integrating Visio diagram in SharePoint
You can access Visio files stored in a SharePoint document library either from the SharePoint site or directly from Microsoft Office Visio 2007.
Accessing files from a SharePoint site provides check-in and check-out capability and the ability to view and edit files. You can edit data by using Internet Explorer or directly within Visio.
When you edit a drawing from the SharePoint site, you are prompted to save and check-in changes or to discard changes when the drawing is closed.

If you want to view visio diagram inside sharepoint, then you need to install Visio Viewer 2007. The Visio 2007 Viewer allows anyone to view Visio drawings and diagrams
(created with Visio 5.0, 2000, 2002, 2003, or 2007) inside their
Microsoft IE 5.0 or later Web browser.
You can use Visio viewer inside a content editor web part by pasting <OBJECT classid ...> </object> into the Content Editor Source Editor. See the demo of Visio Diagram Integration from here
Download Visio Viewer: http://www.microsoft.com/downloads/details.aspx?familyid=d88e4542-b174-4198-ae31-6884e9edd524&displaylang=en
Reference:
http://msdn.microsoft.com/en-us/library/bb229690.aspx
http://www.den-dopper.com/2006/11/07/how-to-embed-a-clickable-visio-diagram-in-a-sharepoint-site/
http://www.wssdemo.com/Pages/visio.aspx