The moving bright red star in the center of this animation is Proxima Centauri, the nearest star to the Sun, at a distance of 4.2 light years in the constellation of Centaurus.
Proxima has a large proper motion and is moving 3.85 arcseconds per year across the sky, so images taken with a year in between easily shows the shifting position.

The image is a composite with luminance taken without IR block filter on 13/05/2010 and RGB data taken on 19/05/2010 with IR block filter to ensure correct colours of the stars. I then took another image around a year later on 04/05/2011 to record Proxima's new position in the sky and created the animation based on this data.

Proxima is a red dwarf star which emits much of its light in the infrared. It is thought that Proxima is a very distant companion to the Alpha Centauri A/B system, with an orbital period of half a million years or more.
Among the known stars, Proxima Centauri has been the closest star to the Sun for about 32,000 years and will be so for about another 33,000 years, after which the closest star to the Sun will be Ross 248. Proxima is presently approaching at a rate of 21.7 km/s and will make its closest approach to the Sun, coming within a distance of 3.11 light years, in approximately 26,700 years.
As seen from Proxima Centauri, the Sun would appear as a bright, 0.4 magnitude star in the constellation of Cassiopeia.
Proxima Centauri is often suggested as a possible first destination for interstellar travel. Nuclear pulse propulsion or other exotic technologies would be needed to keep the travel time within about a century. If current propulsion technology were used, a voyage would take thousands of years and would likely require a ship large enough to carry an entire population that could be used for colonization of a planet.