The capacitor module provides a very short-term fill-in power supply to cater for transient peak current demands. In an application that requires a high peak current this unit saves having to fit a power supply capable of handling the peak current. This may be a desireable feature as the smaller power supply will have a lower short-circuit current limit and lower current rated wiring could be used, for example.

Figure 1. Extract from datasheet.
Some of these datasheets have a high "tease-factor" in that they don't disclose the innards and this can make it difficult to predict performance in non-standard operating conditions.
At its simplest this unit contains a large capacitor (probably several to fit the case style) and a few other components. We can estimate the capacitor value from \$ i = C \frac {dV}{dt} \$. Rearranging and assuming that the voltage might drop, say, 10% over the rate 1 ms at 40 A we can calculate
$$ C = i \frac {dt}{dV} = 40 \frac {1m}{2.4} = 16,600~\mu F $$
This seems quite feasible.
The recovery time is 1 s so there is a resistor or current limiter in series to limit the current draw from the power supply it is supplementing.

Figure 2. The internal wiring showing the charging resistor, the discharging diode (to prevent rapid recharge) and voltage monitoring circuit and relay. Source: CP M CAP Operating Instructions.
In use the capacitor module is simply wired in parallel with the PSU. (See the operating instructions.)