What could this wood be?
Looks suspiciously like "I'll put  board back here to screw the fixture to, and run wire there, with no box" - which would be a fairly major code violation and increase the scope of your work to correct it and make it safe. 

Edit to add:

You can get rid of the board, but correcting the situation will probably involve a bit more than just cutting it out (i.e. you may need to cut and repair drywall, but that's very much in the "relatively cosmetic" sphere, and not so terribly dificult without complicating factors like tiles or a textured finish, especially if your cosmetic upgrade already includes painting.) I'm dubious that you can just cut out the board and successfully mount an "old-work" box there, as the remains of the board would be in the way.