looks like it functions the same way as many motors do with their brushes. the spring itself is the conduction path between the terminals and ensures constant, adequate contacts between the 2 points.
i would imagine the 4 springs go into the 4 holes you can see down the center of the holder then once they are in place, you can compress them and slide the terminals over the top of the springs which then holds the spring in place and ensures good electrical contact.
i think i can see some small grooves either side of the holes in the center, i reckon that's where the terminals would slide into to be held securely. if there's not grooves there, i still think it'd somehow be secured in a similar way to that. if you don't have any luck, take another photo of the holder with either better light or a flash so i can see more detail and might be able to offer a bit more help.