You see, when our Sun starts running out of hydrogen fuel, it will expand until it swallows Mercury and Venus, and potentially even expands into our orbit. Obviously, this means bad things for anything left on Earth. Even if the Sun doesn't grow large enough to reach Earth's orbit, you don't want to hang around waiting for the oceans to boil away and the atmosphere to burst into flame. Trust me, you'll have a bad time.
IMAGE COURTESY WIKIMEDIA COMMONS (CC BY-SA 3.0)
So why study an event so unimaginably far in the future? Because it can give us a better idea of where to look for intelligent life outside our solar system. We've detected almost a thousand planets using a variety of methods around a few hundred stars in our galactic neighborhood. That's all well and good, but if the goal is to find life on other solar systems, finding planets is just the first step.