I read that when stars burst it becomes a black hole. Now will the sun burst one day? If it bursts what will happen to life on earth?
The Sun will never burst and will not become a black hole. Stars end their lives in two different ways: those will mass around the mass of the Sun will end their lives in a gentle way, becoming a planetary nebula and leaving behind a remnant called "white dwarf". Stars much more massive than the Sun explode as a supernova leaving behind either a "neutron star" or a "black hole". So, do not worry about the Sun becoming a black hole.
Now, to answer your second question: If hypothetically the Sun suddenly becomes a black hole (which will not happen), then nothing will happen to the Earth. Black holes do not go about scooping up people and planets. However, as there will be no longer any sunlight, we will have trouble keeping warm.
However, note that we are not safe on Earth forever. In another 4.5 billion years (that is a long time), the Sun will expand into a "red giant" star and will come very close to the Earth's orbit. At that point, Earth will become so hot that there will no longer be any oceans and will probably be the end of life as we know it. However, that is way into the future and right now, there is more danger that we will cause our own destruction (by wars and pollution) than anything happening due to the Sun.
This page was last updated June 28, 2015.