What is this white powder coming out of my baseboard?
It looks like drywall dust. There were probably cuts made with a rotary tool which left dust inside the wall, and now it's working out, possibly due to air pressure in the wall from an HVAC duct or just environmental air surges. 

I'd run a strong vacuum sealed against the joint with rags. That should pull most of it out, though you'll still probably see some residual dust for a while.