The ArcGIS Map Web Part's basemap provides the context for the content that you want to display on the map.  To change the basemap, simply click the Basemap button.  This is located within the Map group on the Application tab.  Then select a basemap from the Basemap Gallery:

The basemap will change to reflect the selected item.  All other content in the map will remain unchanged.

Like much of the functionality provided by ArcGIS Mapping for SharePoint, the basemaps contained in the Basemap Gallery are fully configurable.  Edit the ArcGIS Mapping Basemaps list to add and remove basemaps.

See Also