Alpha Centauri is a star of the southern sky, and is not visible to observers at a latitude greater than about 25° north (roughly the latitude of Florida, Egypt or Taiwan). For those in the southern hemisphere, though, it is not hard to locate: it sits in the centre of the Milky Way, about fifteen degrees east of Crux. In fact, a line through the cross-piece of the Southern Cross (from Delta Crucis to Becrux) points the way to Alpha Centauri.
While most of the sky's more famous stars are known by their proper names (Polaris, Sirius, Betelgeuse and so on), Alpha Centauri is unique among these in being better known by its Bayer designation, rather than one of its two proper names, Rigel Kentaurus or Toliman. Of these, 'Rigel Kentaurus' means 'The Centaur's Foot', and is easy to understand as the name of a star in the southern parts of Centaurus, the constellation of the Centaur. 'Toliman' is a little more obscure: it means 'The Vine-shoot', and refers to the ancient tradition that the Centaur held a rod entwined with vines in his hand.
Its magnitude of -0.01 makes this the fourth brightest star in the sky, but only by a tiny fraction: it is just 0.04 magnitudes brighter than Vega in the northern constellation of Lyra. In fact, Vega is intrinsically a much more luminous star than Alpha Centauri, but this is balanced by the fact that it is more than five times further away from Earth, so the two stars appear artificially similar in the sky. Vega is not alone in being further away than Alpha Centauri: there are no stars closer to our own Sun than those in this system.
The Alpha Centauri system seems to have formed somewhat earlier than our own Solar System ('somewhat' in this context is probably of the order of a thousand million years or so). At its heart, two remarkably Sun-like stars orbit their common centre of gravity roughly once every eighty years. Like our Sun, both stars are relatively stable in nature and, again like our Sun, they are comparatively rich in more complex elements. Alpha Centauri B is an orange star, rather cooler than the Sun, and slightly less massive. By comparison, yellow Alpha Centauri A is close to a twin of our own star. Its spectral classification (G2V) is identical, though the star itself is just a little more massive, and hence a little more luminous, than the Sun.
With these two stars, particularly Alpha Centauri A, being so similar to the Sun, it's natural to wonder whether they might host a system of planets, perhaps even terrestrial planets comparable to our own Earth, as shown in the speculative illustrations on this page. At the moment, the technology to find this out for sure is several years in the future - there's simply no way of knowing whether such planets exist or not. It's perhaps notable that to date not even the more massive planets that we are able to detect have been reported orbiting either of the main Alpha Centauri stars: if such planets are absent, any terrestrial planets within their systems would likely be affected. Without the gravity of more massive planets to attract interplanetary debris, any inner planets of such a system would probably be at rather more risk of comet or asteroid strikes than our own planet. Of course, this is no more than speculation - the actual workings of the Alpha Centauri systems, assuming they have any planets at all, is completely unknown at this time.
Beyond the A and B stars, there is a third component in the system: Alpha Centauri C. This is a tiny, faint red dwarf orbiting the two main stars at an immense distance: roughly one fifth of a light year. This is a Proxima, a star with a faint reddish glow so feeble that it would hardly be visible even from the core the Alpha Centauri system. It seems to be a late-comer to that system, perhaps a wanderer pulled into orbit by the two older stars, but it has one important distinguishing feature: it is the single closest star to our own Solar System. For that reason, though it is properly an outlier of the Alpha Centauri system, Proxima is given its own entry on this site.