DC-DC converters typically convert one voltage (or range of voltages) to another (fixed) voltage.
Converters that take a higher voltage and transform it into a lower voltage are called "Buck" or "Step-Down" converters.
Converters that take a lower voltage and transform it into a higher voltage are called "Boost" or "Step-Up" converters.
For most uses in a Christmas display we would be talking about the buck variety.
Almost all of the DC-DC converters commonly used in a Christmas display will be the non-isolated type. This means that the input and output side share a common 0V wire.
Input Voltage Range
The DC-DC converter will have an input voltage range over which it is specified to work. For example, a buck converter with a 5V output may accept anywhere from 12 to 24 Volts. This means that the input voltage can be anywhere in that range.
For buck converters, the lower input voltage limit will typically be a few Volts above the set output voltage. If the input drops lower than this, the output will no longer be regulated. This may see the output drop proportionally, drop to zero or perhaps become unstable.
The upper input voltage limit is the maximum it can handle without sustaining damage. If you exceed this limit, the converter could fail in such a way as to put the input voltage directly to the output. This is obviously something we want to avoid!
The input power (Watts) is the input voltage (A in Volts) multiplied by the input current (B in Amps). The output power (Watts) is the output voltage (D in Volts) multiplied by the output current (C in Amps).
If the DC-DC converter was 100% efficient, the input power and output power would be the same. In reality the input power will always be more than the output power. The difference is lost as heat in the conversion process.
Here's a chart for a 5V 3A (output) DC-DC converter found on the Internet:
As you can see, the efficiency drops off markedly at low output currents. This means there's proportionally more wasted energy (heat dissipated), but luckily at those lower currents the absolute waste is fairly low.
Also (for this example converter), the efficiency is lower when the input voltage is higher. This may not be the case for all converters though. You'd really need to check the efficiency for the particular input voltage, output voltage and output current on the chosen converter.
This means is that you may need to factor in these losses when calculating the power supply requirements. So as an example, if your 5V load (lights) draws 15W (3 Amps), a 24V power supply would need to supply about 18W of power to the DC-DC converter to make it happen.
This calculation was derived by seeing where the 3 Amp point intersects with the 24V curve in the graph. This lines up with the 85% mark on the vertical axis. We know the output power (Volts * Amps) to be 15W so the formula becomes 15 / 0.85 which is 17.65 (Watts). Furthermore you can then divide this input power by the input voltage to find the input current to get 0.74 Amps (Amps = Watts / Volts).
Because a buck converter draws less current on the input side, you can often use a smaller gauge cable for the run back to the power supply. Or conversely you'll experience less voltage drop given the same wire gauge and length.
A buck converter located near the load (lights) can also assist with minimising voltage fluctuations with a varying load current. This is because the regulation is done close to the load and fluctuations caused by voltage drop in the power feed (input) cable are compensated for by the DC-DC converter.
DC-DC Converters on da-share