Hey mmmboh,
The idea is that CMOS circuits use virtually no current when they're in steady-state. If you have some network of NANDs and all of the inputs are constant, not changing in time, then the CMOS circuit uses very little current. The only current it uses is called "leakage," and it's negligible in most situations. When the inputs change, though, the gate capacitance of the transistors has to be charged or discharged, and that does consume current.
The circuit they gave you is kind of a trick. They're driving the input of the NAND gates to mid-scale, halfway between the two supplies. This is a no man's land, somewhere between logic-0 and logic-1. This voltage is adequate to partially turn on both the NMOS and PMOS devices in the gates, so a continuous (and possibly large) current will flow.
Normally, when a CMOS gate changes state, its output changes so rapidly that the voltages are only in the no man's land for a short time. Except during these brief transitions, the voltage is stable, very close to either supply. Because the transitions are so rapid, the total power loss is very small.
- Warren