If you mean the sun just went “poof” and vanished forever, that would mean. The whole solar system would just fall apart. The moon would still orbit Earth, but all the planets orbiting the sun, including Earth, would be flung into deep space and become rogue planets. Without light or heat from the sun, all life on Earth would end, quickly I might add.
There are, in fact, rogue planets wandering around although not probably because their star vanished in thin space but more likely because they were just flung out of orbit for various reasons. These rogue planets wander in space in total darkness and are very cold, lifeless places in the galaxy.