KIRK: I don't see anything. I can't understand it.
SPOCK: Invisibility is theoretically possible, Captain,
with selective bending of light. But the power cost is
They may have solved that problem.
Spock is impressed that the Romulans have solved the power cost issue. Flashback a century and the Romulans had small invisible mines (with small power sources, yet they worked) and large invisible starships. Later we saw Romulan starships with holographic projectors coving their hulls, which also worked to fool rival ships. The Enterprise NX-01 even had a cloak-equipped Suliban ship on board for months, and used it in a rescue mission, not to mention their prior enounter wth the Xyrillains and their invisible ship. Kirk "can't understand" how a Romulan ship is invisible when the idea of invisible ships, including Romulan invisble ships, is old hat by the 2260's? No way does that fit without extensive loud coughing and fudging, unless they just don't teach history at Starfleet Academy.
The way I look at it is, the TV audience of the 1960's wasn't as knowledgable about all the sci-fi concepts we take for granted today. Kirk and Spock were basically explaining to the audience that there is some scientific basis for invisible spaceships, that it's not just some magic.