According to "The Science of Pokemon" on Tumblr, a charizard's tail flame keeps it warm. Without the flame, the charizard will basically freeze to death, because it has no other way to generate enough body heat to keep it alive. It's because the flame isn't just at the tip of charizard's tail. It burns inside of it's body, because of a stream of gas that passes through him. It seem like the tail flame is the flame that keeps the rest of the gas lit, so if it goes out, the rest of the fire inside goes out, too. It does indicate the health and emotions of charizard, too, but I think that's more of a side effect than something really important.
