There's an implicit "for the best price each room could possibly bring" attached to that goal. The reasoning is basically that the cost of a hotel room (construction, upkeep, etc) is not affected too much by whether it is occupied or not. (In that way it's very similar to a seat on an airliner.) So considering your costs as a hotel operator are nearly fixed, you're quite obviously better off selling 50 rooms at $200 and then 50 more rooms at $100, than if you had kept the price at $200 and only been able to sell the first 50 rooms. Of course in the real world the pricing strategies are a lot more complicated than that and depend on having good models for how many people are willing to pay what price, and when.

I must be missing something here. How does an empty room make any money?

I first realized this concept on much simpler level. In college, my older friend and I were slowing waking up after a very successful party. There was one beer left. And I said, "That would perfect if we had zero beer left". He replied, "No, one beer is perfect. It means everyone got enough. If there were zero then that means someone could have tried to get a beer after we ran out. With one left, we know that everyone got exactly as much as they wanted."

In many occupancy-based price optimization algorithms (at least in the multi-family sector where I previously worked), it is not optimal to maintain 100% occupancy. It doesn't allow much flexibility. I've seen recommendations for apartments around 95% to cope with fee changing, turn over maintenance etc. I'm sure hotels are in a similar situation (but have even lower percentage due to guest volatility).

If a guest knows they can get a better rate they will force you to drive down rates longterm. Also if you sell out, that means you could have charged more and made more in net