Proxima Centauri is a red dwarf star in the Alpha Centauri star system which bears the distinction of being the closest star to the Sun. The discovery about the star's close location was made in 1915, and it has been a topic of interest and frequent observation ever since. Some people feel that when space travel develops to the point that humans can leave the solar system, the Alpha Centauri star system would be a logical place to visit, and that Proxima Centauri would probably be the first stop, although it seems unlikely that the star could support life.
Red dwarfs are stars which are much smaller and cooler than the Sun, with Proxima Centauri having a diameter around one seventh of the Sun's. As a result of their size and relative coolness, they are extremely dim; Proxima Centauri cannot even be observed with the naked eye, although it can be captured on high powered telescopes. This star is also classified as a flare star, meaning that it randomly experiences periods of increased luminosity.
This star is around 4.2 light years away from the Sun. Other stars in the Alpha Centauri system are much brighter, which can make it challenging to observe Proxima Centauri. Equipment sensitive enough to observe the star and generate data which could be used to figure out where it was did not emerge until the early 20th century, and it was only identified as a flare star in 1951. You can get an idea of where Proxima Centauri is if you happen to be in the Southern Hemisphere, as it appears in the constellation centaurus, the centaur. The Alpha Centauri system looks like a single point of light to the naked eye, making the brightest point in the constellation.
Because red dwarfs are so much cooler than the Sun, they don't provide much hope of life. In order for a planet in orbit around Proxima Centauri to sustain life, it would have to be extremely close to the star, creating a situation in which it would be tidally locked. When planets are tidally locked around stars, one face of the planet always faces the star, creating a situation where half of the planet is always in darkness. In another example of tidal locking, the Earth's moon always has one face towards the Earth.
If Proxima Centauri does support planets in a tidally locked orbit, it would be challenging for life to evolve on these planets, as it would have to contend with temperature extremes on the two faces of the planet. The organisms on the planet would also have to deal with periods of sudden and extreme brightness every time the star flared, making life on the planet rather uncomfortable, in all probability.