Why are APU engine generators rated in kVA and not kW?
Current and voltage don't always vary at the same time, one usually lags, this lag is the root of evils found in electrical engineering.

Any device is a mix of resistive load (no lag), inductive load (current lags) and capacitive load (voltage lags).

The lag (phase shift angle) is denoted with Greek letter φ, and usually expressed as cos φ, or power factor. Power factor $=100 \cos φ$. Each device has its own individual φ, which may vary with conditions.

Lag effect is only visible when voltage or current changes. This happens transiently in DC when the circuit is closed or opened (effect used to create high DC voltage from low DC voltage in a contact breaker), but constantly in AC  (not mentioning other induced variations, e.g. changes in mechanical demand on an electric engine will change the impedance of the coil, so the current). The effect of the phase angle increases with circuit frequency, and is significant in aircraft circuitry, with major loads working at 400 Hz.

With this lag, the voltage and current mean (RMS) values are not sufficient to size electrical circuits. A phase shift introduces additional power in the circuit. This reactive component is not described by the RMS values, it's only visible when looking at instantaneous values, for example on this animation of the addition of two phasors, where the fixed circle radii indicate the mean values, and the moving dots show the instantaneous values. In simple cases one can determine the power required using the triangle of powers:


(Triangle of powers, source)

The apparent power is the sum of the real part of the power (resistive load in W) and the imaginary part (reactive load in VAr).

Work (Joule) is only produced by active power (the reactive power produces no actual work) and the active power rating of the generator must be higher or equal to the active power rating of the load. However the reactive power produces a reaction on the generator (by phase shifting the current) and must be accounted for when sizing the generator. The generator must have an apparent power rating higher or equal to the apparent power rating of the load, at the working phase angle.

A higher apparent power, regardless of the active power, requires a more robust generator and wiring to prevent overload.

One way to simplify the required power calculation is to just add the apparent power value of all devices (in VA). The result in VA or a multiple like kVA is conservative. This allows to select the generator required, provided we know its VA rating too. This is why generator manufacturers provide this value.



Notes:


All units, VA, VAr, W, are of the same kind (dimension of power, W). VA and VAr denote the fact that voltage, current and power are not varying in-phase in AC circuits. These units describe the kind of "power" we are taking about.
When the apparent power rating (VA) is the only rating known for a device, the active power rating (W) can be assumed to be no more than 60%, however the actual value depends on multiple factors and this is only a quick approximation. A generator must be provided with a chart showing the relationship between VA and W under different conditions of use.
A generator cannot work under any power factor, and cannot maintain the same efficiency across the valid power factor range. It is provided with a table or graph showing the acceptable conditions. For example, for this generator, the power factor must be kept in the green area (inductive load, between 80 and 100%), and will start being unreliable at some power factor, depending on the active power delivered and the type of reactance (red area).


(Source)
The explanations above are really simplifications, because in AC, the phase difference is only one side of the problem of reactive power. The other side is the presence of harmonics which are per definition out of phase.

The general principle in electricity is that voltage is set by the generator, and current is set by the load. The load can set a current which has the same frequency than the voltage, this is what we assumed for the answer. However most of the time the load sets a current variation which doesn't coincide with the voltage frequency and/or shape.

This non-linearity between current and voltage creates 'harmonics' and unbalances phases (so a current start flowing in the neutral, which is not something we want).

A little story about that relates to first datacenters in years 1990. Standby generators (diesel) not well sized were unable to sustain computers loads, due to a capacitive reactive power created by computer switching power supplies (non linearity and a cos φ as low as 0.6) Fires ensued, it was time to understand how to deal with apparent power.
The $φ$ angle just comes from the general definition of a sine wave current. Current at time $t$ is defined by $a = a _{peak} \space sin \space (\omega t \space + \varphi)$ where $a _{peak}$ is the maximum current, $ω$ the angular frequency (314 rd/s for the EU grid) and $φ$ the phase shift angle.