To export multiple artboards go into the Export Artboard dialog.
Click on the Advanced link button.
In the Export options row change from the default Selected Artboard to Selected Artboards or All Artboards.
Selected Artboard - Export the selected artboard
Selected Artboards - Export the selected artboards
All Artboards - Export all artboards
Exporting the selected artboard does just what it says. What artboard is selected (or the artboard of the selected layer) when the dialog opens is the artboard that will be exported.
It's shown in the upper right hand corner:
To export a specific set of artboards you must select the artboards and then open the dialog. You only need to select multiple artboards once.
The last artboard you select will be the one that you can refer to later to restore your export settings.
In the Export Dialog select the Selected Artboards option,
Set the export type as either multiple pages or single page.
When you chose Selected Artboards the number of selected artboards is shown next to the artboard name in the upper right hand of the screen.
The export dialog header will change from, "Export Artboard" to "Export selected artboards to multiple pages".
Each artboard has it's own export settings. If you switch to another artboard those settings will be used.
The Global options, when checked makes it so you can use one artboard for all export settings.
Click the Export button to export multiple artboards. The export process takes longer so please wait while it exports until the Export Complete message shows.