Note that this does not simply shift the centre, but instead draws the display as if the chosen body is fixed in position and all of the other bodies are moving relative to it.
The default is "Grid Origin" - that is, the zero point of the X, Y, Z coordinate system. In the saved examples which come with Gravitorium, the Sun sits at the grid origin and moves so little you wouldn't be able to tell the difference between a display centred on the grid origin and one centred on the Sun:
If you choose another body, however, the display can appear very strange. If you choose the Earth in the solar system simulation, for example, you get a view of what things would look like if the Earth really did stand still:
This is a good demonstration of why, seen from the Earth, some planets appear to undergo "retrograde" motion against the background of the stars.