Why does my Battery light come on and the headlights go from high to dim

Agree with answer #1... In addition, this sounds like an intermittent alternator/charging system problem that needs to be checked/tested while the symptoms are occurring! .. However that can be difficult since it is.. well... intermittent!!... The volt meter suggestion would your best bet, as you could check this as it is occurring, provided it acted up long enough for you to do so...