Exoplanets (consider it as a short version of Extrasolar planets) are those planets that are not from our solar system. They orbit around their own Sun like star. According to Wikipedia there are more than a thousand such planets that have been discovered. 1 out of 5 Sun like starts have planets that resemble to our planet Earth in habitable zone .
There were theories from centuries ago about the existence of exoplanets, in 1992 first exoplanet was discovered and it confirmed that they do exist. Astronomers and scientists have discovered lots of Earth like planets having similar properties. Among all of the exoplanets discovered, most of them are Jupiter sized because it is easy to find out a bigger planets than smaller ones.
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How do astronomers find an exoplanet?
Discovery of exoplanets is not easy because they are revolving around a brighter star. Even if we get vision of such planet for a moment we have no guarantee that we’ll still be able to see it next moment.
e.g. You’ll see almost nothing if you have a small object in front of a large light source (small object between you and the large light source).
Because of this reason no one can easily discover/find exoplanet directly. There are indirect methods to discover these planets. One of those is called Transit method.
Brightness of star is measured for long period of time. When a planet crosses from the front of the star, it also takes away small amount of its brightness. This loss of brightness is measured carefully to get results. Some other tests are also performed to confirm exoplanet.
How exoplanets are named?
Name of an exoplanet is given by taking the name of star around which it is orbiting and then adding a lowercase letter to it e.g. Kepler-78b etc.
First planet gets the designation of b and planets that are discovered later gets succeeding letters i.e. c, d… etc.
Why we are finding more exoplanets?
Scientists and astronomers think there are chances of extraterrestrial life  on some other exoplanets in habitable zone. Up till now no extraterrestrial life has been discovered because exoplanets are far away from us. It is hard to find out life from that much distance. Maybe someday we’ll visit some exoplanet supporting life, light years away from us.
Sources: Cover image(NASA), Wikipedia and some others.
 = The region around a star within which planetary-mass objects with sufficient atmospheric pressure can support liquid water at their surfaces. (Wikipedia)
 = Extraterrestrial life is defined as life that doesn’t originate from Earth (Alien life). (Wikipedia)