It's not that a DCDC (Buck Regulator) saves power, it's that an LDO wastes power.
In effect a buck regulator converts the voltage difference to more available current.
An LDO converts the voltage difference to heat, and heat is a waste product you don't really want.
An LDO regulating, say, 12V down to 5V has to drop 7V and dissipate that power as heat. The more current you draw the more heat is produced. If you draw 1A through that example (5W) it in turn draws 1A from the power source (12W), so it has to lose 7W of power to the atmosphere.
A perfect (they don't exist, but for illustration) buck regulator going from 12V to 5V, with 1A output (5W) would draw in turn 5W from the power source, which at 12V would be 417mA.
Of course, as I say, perfect buck regulators don't exist and there are still losses, so it would actually draw slightly more from the source - more like maybe 6W, or 500mA. Still considerably less than an LDO.
There are down sides to buck regulators though:
- The are noisy. They work by rapidly switching the power on and off, and that makes for higher radiated and conducted emissions.
- They are harder to lay out. To keep the EMI emissions low and get them to pass compliance testing, careful layout on the PCB has to be considered.
- They use more components. An LDO typically is one chip and a couple of capacitors. Buck regulators also need (normally) at least a diode and an inductor as well.
All that adds up to buck regulators being more expensive than LDOs.