The Help section of ArcGIS Explorer Online describes the site like this: "ArcGIS Explorer Online is an online application that lets you explore and present maps within an efficient and well-structured environment." This site is different from ArcGIS.com in that ESRI considers ArcGIS.com a lighter version of ArcGIS Explorer Online. Also, ArcGIS Explorer Online requires the Microsoft plug-in Silverlight.
Note: Free ArcGIS Online accounts do not work with Explorer. It seems that Explorer only works with Enterprise or Corporate accounts.
This Introduction is almost an hour long. However, by the end of it, you should be able to navigate ArcGIS Explorer Online successfully.