How do I export SVG images from multiple artboards in a batch process using Adobe Illustrator CC
If you're using CS6 (not sure about earlier versions) then you need to save as SVG, there is no SVG export option.
File → Save As → SVG (svg)
In CC there is a new export option for SVG.
File → Export → SVG (svg)
In both cases, make sure to check "Use Artboards" to export the contents of your artboards as individual SVG files.