Kardwill: Note : The objective is not to completly conquer the map, but to eliminate every opponent by capturing their homebase. You can ignore 80% of the map and still win if you manage to make a beeline to the enemy HQ and succesfully sieging it.
Yup. You never need to 100% explore every province. You also don't need to clean out every "lair" in provinces. I almost always leave some lairs unharvested even in my demesne (home province) at end-game. As was noted above, you win by knocking out the rival AI players, which you do by conquering their home castles.
Your score (defined as "Glory" once you get past the tutorial mission) is determined by a bunch of different things, but if you take too long to conquer a Shard, you can get a time penalty.
It's a balancing act between exploring your home province (which gives
very modest experience to your hero and allows your town to grow larger and larger), harvesting the toughest lairs that you can survive without major casualties (which yield one-time gold, gems, and hero goodies--as well as a lot more XP), and conquering new provinces (which yield gold, gems, and more locations to explore if you have the time).
As a general rule of thumb, your Heroes are the tip of your spearpoint. Level them up whenever you can and plan your
long-term building strategy around what will turn them into killing machine as quickly and cheaply as possible.