Variation was also a part of MOSS 2007and now is also a part of SharePoint 2010 with some added features.
Variations are used when we would like to create multi lingual SharePoint sites. There is not much information available about variations but I will try to cover as much as possible.
You can find variation settings under site collection settings. Variation, Variations labels and variation log.
Variation operations execute on the back ground timer jobs in SharePoint 2010. If you see under Job definitions in Central administration, you will find different jobs running for variations.
We here need to create variation labels and hierarchy and define the source site and then these settings for variations will be replicated for all targeted sites.
Variations can also be set programmatically. We have not explored this very much however whenever we get a chance to explore this, we would love to post it one more time with more information with example.