There are two things which affect how bright a star appear from Earth. One is how close it is, and the other is how intrinsically bright it appears. Alpha centauri is not intrinsically a very bright star. It has an absolute magnitude of 4.4 only, which means it's slightly brighter than that Sun (which has an absolute magnitude of 4.8 - bigger is dimmer with magnitudes). The brightest star known is Sirius though, which is about twice as far away as Alpha Cen, but has an absolute magnitude of 1.4 (which means it is instrinsically almost 40 times brighter). See the Stars and Constellations website for further explanation of magnitudes.
Karen was a graduate student at Cornell from 2000-2005. She went on to work as a researcher in galaxy redshift surveys at Harvard University, and is now on the Faculty at the University of Portsmouth back in her home country of the UK. Her research lately has focused on using the morphology of galaxies to give clues to their formation and evolution. She is the Project Scientist for the Galaxy Zoo project.