The following scenario would happen on occasion during my previous suburban commute. I'd be stopped at a red light on a 6 lane (3 lanes each way) 45 mph road with a bunch of other traffic. Then the light would turn green and everyone starts moving. Of course, the cars get ahead, because I can't go 45 mph.
About a block ahead there would be an opposite direction motorist waiting to turn left into a residential or other minor street. He can't turn left because of the traffic that just got the green light is approaching. Once he sees that the last car in the "pack" has made it by, he starts to make his left turn, but he didn't see me when he started making his turn.
I have found through experience that moving left in this scenario makes the driver more likely to either (1) stop and let me through the intersection, or (2) complete the left turn faster so that I can keep going without slowing down too much. Whether the lateral movement makes me more visible, or moving further left lets him know that I'm a 20 mph bicyclist and not the usual 10 mph bicyclist in that area, or gives the impression that I will pass him behind his rear bumper, or perhaps all of the above - I honestly don't know. I do know that there were some times where I didn't move left in that situation and I found myself braking hard (and I remember quite well because rode a fixed gear on that commute).
My current suburban commute is in a newer area where all left turns must be done at a light, so this situation never happens anymore.