System Transfer is functionality that was added with the 2.0.0-2 June 6/7 2011 system update, which allows you to transfer DSiWare, recorded audio from the Nintendo DSi Sound title, "internal memory" pictures, WFC configuration, from DSi to 3DS. On DSi this is done with the "Nintendo 3DS Transfer Tool" that is downloaded from DSi Shop, while on 3DS System Transfer is accessible in the System Settings. System Transfer can also be used to transfer 3DSWare to other 3DS systems.
DSi System Transfer
With the DSiWare DSi->3DS transfer, savegames are not transferred. When transferring DSiWare, the DSi system transfer title will send a SOAP request to the DSi Shop server, this transfers the DSiWare license/ticket to the 3DS shop account. The DSi title will then delete the ticket from NAND. The 3DS will then download the ticket, tmd, and content immediately from shop/CDN.
3DSWare Transfer
3DSWare transfer isn't available yet, would be implemented in another future system update.
See also
Nintendo of Japan System Transfer page.