Actually, the sun is only at the centre of the Solar System, which is less than a mere pin prick on one of the outer arms of the Milky Way Galaxy. The Milky Way itself is only one of trillions of galaxies all moving around the universe at incredible speed.
So there's probably not much significance there at all.
As mentioned, the sun will be at the center of the GALAXY. It is a given that the sun is at the center of our solar system.
http://en.wikipedia.org/wiki/2012
John Major Jenkins and others [11] believe that an alignment will occur when the sun rises above the horizon on December 21 2012, at which point the sun will rise in the middle of the Milky Way Galaxy, thus causing an alignment between the earth, sun, and the Galactic Center. [12] It is suggested that this event will cause numerous changes on Earth. However, the event is only a visual phenomenon from the Earth's perspective, which is caused by the precession of the equinoxes or the 26,000 year wobble of the earth, and thus only changes our perspective, not the actual position of the earth in relation to the galaxy. In short, there is no gravitational force or radiation to be expected from this event because other than the tilt of the earth; nothing will be any different from what occurs in any other solstice. [13] [14] [15]
Michael Tsarion [16] and others think that an actual physical alignment of our entire solar system will occur with the horizontal plane of the Milky Way Galaxy on that day. The solar system is moving around the center of the galaxy every 225 million years or so, and while doing so is moving up and down in a cycle crossing the plane every 33 million years. According to the Journal Nature, however, there is evidence of the solar system crossing the galactic plane 3 million years ago. This would mean that we are moving away from the galactic plane, not toward it, and we will not be due to cross it for another 30 million years. [17]