What is the effect that makes components on a circuit board move into place?
It's just the surface tension of the solder in liquid state.

A physical system will settle in its lowest achievable energy configuration. Given the surface tension of the solder and the adhesion forces to the different surfaces it is in contact with, the lowest energy configuration would be all the component pins in the center of their respective pads. Of course, this assumes the presence of a solder mask and the resultant force overcoming any friction present.

It is the same principle that generates the meniscus of a liquid in a container.