Proxima Centauri is a member of a triple star system that includes two other stars, Alpha and Beta Centauri. It's located in the southern-sky constellation of Centaurus and is roughly 4.4 light years away -- the distance light travels in four and a half years. This triple star system is our closest stellar neighbor. While Alpha and Beta Centauri are roughly the same size as the sun, Proxima Centauri is what's known as a red dwarf.
According to the European Southern Observatory, Proxima Centauri is about 4.85 billion years old. Like other stars, it formed from a collapsing cloud of gas; this collapse generated enough heat to initiate nuclear fusion, which thereafter became the source of energy for the star.
In general, the less massive a star, the longer it will live. Very massive stars burn through their available fuel rapidly and explode in what are called supernovae. Smaller stars like the sun enter the red giant phase once they've exhausted their available hydrogen and start to fuse helium instead. Proxima Centauri is a red dwarf and so will never enter a red giant phase; instead, it will become a blue dwarf and slowly run out of fuel before it gradually fades away. None of this will happen soon, of course -- Proxima Centauri will continue to shine for trillions of years from now, long after Earth has ceased to exist.