well, 5 things.
1.we wouldn’t notice…at first.
the sun is 8 light minutes away from earth. that means that it takes light 8 minutes to reach the Earth. in other words, if you were standing on earth, and your friend were standing on the sun…(NEVER DO THIS)
…and your friend waved to you, you would see him wave to you eight mins after he actually does it. so, you would see the sun disappear 8 minutes after it actually does. also, gravity “travels” at the same speed light does, so the Earth would keep orbiting where the sun was until 8 minutes after!
2.it would be very dark.(obviously)
the sun going out would mean that it would be very dark. the people on the night side will notice that the moon went out. stars would be the only source of light outside of our planet. photosynthesis would stop, and plants would stop making oxygen. that sounds bad, but it’s not a problem. the life on earth would still have enougf oxygen to breath for another 1000 years or so. there is a bigger problem though…
3. it would be very cold.
the planet would cool very quickly. after a week the temp would drop to 0℃. after a year, we would have to go underground to survive.
4. the ocean would freeze over
so, the ocean would become the biggest skating rink in the world! but only the surface. the bottom won’t be frozen because of hydrothermal vents.
5. some organisms would be just fine!
spoiler alert: not us. only the ones that live around hydrothermal vents would survive. cool!