A constant power load varies it's impedance on change of input voltage to keep the power constant. A constant impedance load is simply a load that presents an unchanging impedance, like a resistor. An L-Pad is used to change speaker output level whilst maintaining a constant impedance load to the amplifier.
A good example of a constant power load is a switching regulator. Since this has to maintain it's power into it's load, it must draw the same power from it's source even if the source changes voltage.
This is also an example of a negative impedance because in order to maintain the output power, if the voltage in drops, the current must rise (opposite to a standard resistor where the current and voltage rise/fall with each other)
Here is an example circuit, made from a LT1377 boost switching regulator:
Here is the simulation:
The input voltage V(in) (blue trace) starts off at 4V, and gradually rises up to 10V. We can see the power (red trace) stays constant at ~1W over a change of 6V at the input (it's not perfect as it's meant to represent "real life" and not 100% efficient, but it's pretty close)
We can also see the dynamic negative resistance characteristic (green trace) which is due to the input current falling as the voltage rises. Tt falls from ~300mA to ~120mA over the voltage rise from 4V to 10V - don't be confused by the minus sign, that's just the direction of measurement in LTSpice.
The dynamic resistance slope can be roughly calculated by (4V - 10V) / (300mA - 120mA) = -33.3Ω. Looking it another way, 6V / -33.3Ω = -180mA.
Both walk together. Imagine voltage to be, as the name says, potential. In other words, is what your source can potentially causes in your circuit. It is its potential to generate a current. As the ohms law states (U=Ri), we can think of current being a consequence of a resistence connected to this source. This is almost a rule for almost every source of electricity in our days, but there are exceptions (below)! So, whenever you think of your wall outlet or a car battery or a cellphone battery, they have a voltage potential and the current will be calculated by which material or what are you connecting to the power source (by its resistance). Generally, the current specs tells us what is the MAXIMUM current that this power supply can handle. But it does not tell you that this source will be always +V volts and A amperes!
But note that this is the case for voltage sources. As the name says, it guarantees a constant voltage (ideally). So you calculate current because you know that the nominal voltage will remain the same.
So the excepetions will be current sources. Now everything is inverted! This kind of power supply guarantee's that the current will remain fixed. So you can calculate what voltage it is applying to your circuit so it can delivery that amount of current (also by ohms law) but generally we do not need that. Although a current source concept is very useful inside electronic devices, we are not used to see them in our days. But one good example is your telephone line comming from the wall. Those are current sources. Note that you cant damage the wires or the telephone company by making a short circuit to these wires. You can connect a multimeter and you will see that the current will be stable at some point (here in Brazil at 24mA). I can connect a 10Ohms resistance or a 300Ohms resistance and the current will be the same. Of course the voltage applied will be different, and that is how a current source works.
So it all depends on what type of source you are dealing with. If it guarantees a current fixed, you can calculate the voltage difference between terminals. If it guarantees a voltage value, you can calculate its current depending on which load you put there. In most cases, those power supplies from computers, cellphones, etc are all voltage sources and its specifications guarantee a nominal voltage and a maximum current. But don't expect to have that current regardless of the connected load!
Most power sources are constant voltage, and not constant current. If you take the two main sources of electrical energy, which are batteries and rotating generators(regardless of size), the one thing in common is that their voltage is fixed theoretically to a certain value and can be controlled. For example, a standard AA dry-cell battery has a voltage of 1.5 V, which it will always produce more or less (disregarding real-life errors). The internal chemistry of most batteries relates the internal chemical reactions to the output voltage of the battery. Similarly the generator, for a given magnetic field strength (called excitation), and a given speed, will produce a fixed voltage at its terminals(again, only approximately due to real-life).
In almost any electricity-using device, in almost most cases, a voltage is the cause, and the current is the effect. Only when you apply a voltage to a device, may current start flowing through it (superconductors not-withstanding). Even constant current devices monitor the current and regulate the voltage as per the load. You never hear of a 3 V flashlight battery monitoring the voltage at its terminals. This is due to basic physics, in which change in movement of electrons (i.e. current) is possible when electric field (i.e. voltage) is applied.