Cut in two by a decisive military battle, the first half of Elizabeth I is a story of pressure and uncertainty. England's a weak little island nation with no powerful friends (because, you know, they're Protestant). The Queen -- who's in a constant fight for her sovereignty -- doesn't have a husband and thus cannot birth a proper heir. That doesn't mean, though, that she can't get hers. No, she's got a little side thing with the Earl of Leicester (a doting Jeremy Irons). He's a good companion but a crappy general. This creates problems.
After the defeat of the Spanish Armada, an event the film rightly treats as a complete shock to everyone in England, the second half of the film finds the country suddenly among the most powerful in Europe and finds the queen with no real questions left to answer. The relative lack of trouble without allows her to turn her attention inwards, and, like the creepy old monarch she is, Queenie goes about wooing a young dude, which creates a whole new set of problems.
Aside from the performance and the interesting way the fortunes of everyone in the film hinge on an event that we never see (the total destruction of the biggest fleet of war ships ever assembled up to that point), Elizabeth I is powerful because it's a normal human life given a grander scale. Elizabeth's mistakes are obvious and painful and made for very human reasons. The changes she's able to effect are noble, but it's the habits she's unable to break that make her an endearing figure.