Apparently they are "Disc information file created by AVHCD video recordings; contains information about the file contents in a specific directory; commonly seen as index.bdm and movieobj.bdm; located in the AVCHD/BDMV directory of a media storage device." They are created when the card is formatted. I don't need them since I don't use the video mode.
Since I get Photo Mechanic to put my ingested files into folders that contain the date that the picture was taken, I get folders containing only these files named with the date that the card was formatted. They are a pain, because they need admin permissions to delete and can't seem to be deleted over the network.