Sun will die when all of it's hydrogen will finish. Before dying Sun will be red giant making Earth lifeless in around 1 billion years. Then the Sun will collapse in radius to become white dwarf. White Dwarf is a dead star, if our Sun was big enough then it would have formed black hole. Our Sun has around 5 billion years to live from now.
So this is why we must start to colonize something out of the solar system to live forever till the end of universe.
