The keyword Microsoft uses for Visio 2010 is diagramming.  This is exactly what it sounds like.  It may just be due to my English degree, but it put me in mind of diagramming sentences in grammar class back in grade school.  We broke out the component parts of sentences-- clauses, parts of speech, etc.-- and organized them logically.   Diagramming in the Visio world is simply doing the same thing with business processes, organizations, etc-- so to a Concurrency consultant that means business process mapping, structure mapping (think organizational hierarchies and site architectures) and the like.

Visio Services are now available right within the SharePoint interface ("Visio Web Services")-- you can build the Visio model on SharePoint, based on live business data.  It's available both in hosted and non-hosted SharePoint and is included in the 2010 Enterprise CAL.

Visio will be able to display business data in visual format (think Excel and KPIs) in a more interesting / alternative way; SP will allow you to share Visio diagrams with non-Visio users.  Visio can be used for much more than just drawing pictures-- now it's a BI tool as well.  Data sources can be as intuitive as another SharePoint list.

If you can use Visio, you can build these models, displays  and reports. They call this (duh) data visualization.  

In session at SPC 2009 this past October, I got to see examples in Visio of process models and hierarchy maps, obviously-- but also:

• Sales team reports and forecasting
• Live ski lift status displayed on a photo map (think Google traffic flow mapping—and yes, I don’t like them much and think they’re out to kidnap all of your information for their own nefarious purposes, but it’s a good example)
• Spatial and geographical data (maps-- think the red/blue state maps the talking heads continuously point to on Election Day)
• Manufacturing plant floor layout with metrics/measurements of the various departments, the machines and their production
• Value stream map - manufacturing process broken down by cost per unit - in Visio, diagram is connected to live data

Because Visio has so many templates already in house, the time to produce a Visio model may well be fairly quick if we can take advantage of the available tools.  Obviously, in every case you will need to customize to some degree, but the template library has the potential to be a real cost saver.