I think what they are talking about is something like this:
http://ruggedcircuits.com/html/circuit__13.html
When the capacitor has charged it can power the circuit for a while, depending on its size.
However adding in the charge-pump gadget (not quite sure where that would go) you could use more of the capacitor's power. Say the capacitor starts at 5V, and starts discharging, the processor might cut out at 3V (say). But with the other gadget that boosts the capacitor's voltage back to 5V so it lasts until the capacitor has almost completely drained. Well that's the theory I think.