Partly that's due to clustering: They produce hundreds of Merlins per year vs their competitors which only produce like a dozen or so (often less) engines per year, so just from the learning curve they can save a lot of money.

And unlike essentially every other rocket in the industry, the two stages are largely similar, using the same pressurization scheme, same propellants, same diameter tooling, just differing by the length and number of engines (the Merlin Vacuum engine is significantly different than the Merlin 1D sea level engine, but same underlying cycle type and same heritage), so it's almost like they only need to maintain half the production line as their competitors and get the economies of scale of producing more of the same thing. Also, they're reusing the vast majority of the hardware on roughly half their flights, now, which is, unhyperbolically, a game-changing development in commercial space launch.

SpaceX has a LOT going for them right now. Falcon 9 is a very inexpensive launcher given its performance.

The thing about rockets is that there's a huge advantage in having a higher launch rate. If you're not launching a lot, you're still paying most of your labor and facilities cost just to sit idle. And SpaceX, just producing a single rocket family that is launching more than anyone else in the world (and reusably), is at an enormous advantage there.

We used expendable rockets for Apollo. And there were at least 6 different stages, depending on how you count (3 stages for the Saturn V, plus the command module which had a propulsion section and a reentry module plus the lunar module which had descent and ascent stages), all of which were expended. There were at least 3 different propellant combinations with even more engine types. All of these components were basically dedicated to the Apollo program and had to be paid out of that budget. Each mission requires the expenditure of all those stages.

The BFR for SpaceX, on the other hand, is just two stages. The two stages are very similar, using the same propellant type and basically the same engines. BFR will be used for satellite launches initially, so its development can be paid for separately. The advantage of BFR is that it is fully reusable, so you literally can use the same rocket to send stuff to Mars as is used for satellites. The biggest part, the booster, never needs to leave a few hundred kilometers from the launch site, and can be reused for satellite launches. SpaceX is able to get by with just two stages because they simply refuel the landable upper stage again and again instead of dropping stages. They're leveraging reuse not just to lower launch costs, but to dramatically simplify their mission architecture (and thus reduce development costs).

The reusable upper stage also serves as the lander, once refueled. And it is designed to be refueled by an essentially identical vehicle. And the lander itself can also be reused for the next Mars window. So in a single Mars mission, NOTHING needs to be expended, and at most you're just tying up a single stage during the duration of the mission; the rest of the architecture elements can earn their keep launching satellites while astronauts are on Mars.

Before SpaceX, launch costs for the US were around $20,000 per kilogram to LEO. SpaceX's F9 and Falcon Heavy have brought the cost down to around $1000-2000/kg. BFR, since it's fully reusable, could bring the costs down to $100/kg or even $10/kg. SpaceX designed an architecture that could reduce the cost to Mars by orders of magnitude and whose primary components can be developed and paid for the same way Falcon 9, Falcon Heavy, and Dragon are paid for (i.e. by delivering cargo for paying customers).