The diagram below (steampunk version) suggests some of the issues that a designer has to deal with using the LTC3108. In this case, a thermoelectric generator (TEG) converts heat flow into low level voltages (20 mV to 400 mV) and moderate currents (10's of ma).
The main idea is that there's a low level source of energy at voltages that the LTC3108 can transform into higher level voltages useful for powering microcontroller units and radios and so forth. Unfortunately, this doesn't come for free. The conversion efficiency can vary anywhere between 5% to 40%, which means input losses in power from 95% to 60%! That may or may not be a problem depending on the available ambient energy.
When the unit starts up, the storage capacitor is charged to 5.5V at a rate determined by the available current (power) from the input source. The external circuitry (microcontroller, etc.) draws it's power from the LTC3108, but only sustainably if it the power required is proportionate to the input power given the efficiency. If the input power goes away, the exteral circuitry draws power from the storage capapcitor and the output voltage is regulated until the storage capacitor drops in voltage to the same level as VOUT (normally 3.3V).
Perhaps a more common mode of operation for the external circuitry is to remain in a very low current (power) sleep state most of the time, coming alive periodically to take measurements or do other work and the to return to the sleep state. During the time the circuti is "awake" it draws current (power) from the storage capacitor at a rate that may greatly exceed the capacity of the LTC3108 to deliver from the input source, however, as long as the external circuit awake state is shorter than the time it takes to drain the storage capacitor, all is well. Sizing the storage capacitor to the intended external circuitry is a critical part of using the LTC3108.