Trying to change a lightbulb out of a ceiling fixture
See that dimple in the third photo? I' guessing that there are three or four of them. They engage with slots in the other half of the housing. 

Rotate the lower portion counter-clockwise roughly as far as the dimple is long and it should come down. You may have to align the screws on top with their slots as well. Loosen the set screw to avoid scratches.