If the sun were to blow up, life on Earth would certainly end. It takes eight minutes and twenty seconds for light to travel from the sun to the earth, so we would not know that the sun had exploded until eight minutes and twenty seconds after the explosion occurred. Most of the energy from such an explosion would be traveling at the speed of light or nearly as fast, so life on Earth would end pretty much as soon as the first of sign of the explosion arrived.

However this isn't something you should worry about. The sun has been burning very steadily for 5 billion years or so, and won't change very much for another 5 billion years more. The processes by which stars change is quite well understood by astronomers, and our sun will not explode even after 5 billion more years (only very heavy stars explode) - it will slowly get bigger, and then slowly get smaller and gradually emit less and less heat.