That would be bad! Currently, the temperature of the earth is set by a precise balance between energy coming in from the sun, and energy leaving the earth and going into space by a process called "radiation". The sun's light heats up the surface of the Earth, and at the same time the earth radiates energy out into space. The rate at which the sun heats up the earth is exactly balanced with the rate at which the Earth gives up heat into space, which is why the temperature on Earth stays fairly warm (compared to space, at least).
If the sun suddenly stopped shining, the earth would continue to radiate heat into space, but there would be no incoming heat from the sun and the Earth would quickly cool down. Within a week, it would be below freezing (0°C) almost everywhere on earth, andmost of the water on earth would freeze. Most life on earth would die from the cold and the lack of sunlight, and humans would have to stay inside insulated buildings burning fuel to stay warm. As the weeks and months continue, it would get colder and colder. Within a few months, the air itself would turn into a liquid and eventually freeze into a snow-like substance. At this point, humans could not go outside for even a minute without freezing. The only way people could survive would be by staying in insulated holes in the ground and constantly burning fuel to stay warm. We would also have to use our heat source to constantly melt and boil air from outside so that we could breathe! Eventually, even the best-prepared humans would eventually run out of food and water.
Fortunately, we don't have to worry about any of this, because the sun won't suddenly stop shining anytime soon. In fact, will take billions of years for the sun to run out of fuel and eventually die off.
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