To use the Visio Graphics Web services Service Application you will first need to create a Visio Graphics Service Application. Follow these steps to create a Visio Graphics Service Application and proxy Service application.
Once this process is complete you will be able to display Visio drawings from a SharePoint Visio Web Part. You will need to save the Visio document into a .vdw format which is the web drawing type suitable for SharePoint
Also, make certain you start the Visio Grahic Service in Central Administrator > System Settings > Servers > Manage Services on Server