The traditional solution is to have a range of plants: cheap inflexible ones through expensive flexible ones. You use the cheap plants for your "base load," the amount of electricity that is always needed, and then as you need more and more you turn up the more flexible plants, ready to turn them off again when they're not needed. Not only are these "peak load" plants more expensive, they also tend to be less efficient: could we stop running them?

With the current setup we definitely need them. Power consumption is variable, and these flexible plants form an essential role matching supply to demand. But what if we matched demand to supply? This is an idea people have been playing with for years in various forms. We already have it in some ways: some industrial users have agreements with their power company where certain circuits can be shut off at times of high demand. And there are ideas for more: maybe we let the price of electricity vary based on marginal cost and let your appliances see prices and decide when to run? Maybe the batteries of plug-in electrics can store power at low-demand times and release it at peak times? All of these require the cooperation of multiple parties, however, so a power company can't just apply them on their own. And that's where bitcoin could come in.

In this case we can think of bitcoin mining as a resistor that makes money. Lots of little ASICs run SHA-256 searching for hashes that are small enough, and if you're the first to find one you get some bitcoins which you can then sell. So you still run your base load plants and your load-following plants, but you run them at a higher level, a little above what you think the most power demanded will be. Then instead of using flexible plants to increase supply when it's most needed you decrease your bitcoin mining.

Because power companies are very conservative and bitcoin is new and volatile, you probably start off doing this as a startup that offers a service to power companies: "tell us exactly how much power to consume and we'll do that, but don't charge us much for the power". Because the main cost in bitcoin mining is the electricity, with lower power costs you should be able to produce bitcoins competitively.

(Why not run more traditional batch computing jobs? The main advantage of bitcoin for this purpose is that the startup/shutdown cost is extremely small. The main electricity consumer is hashing hardware, and this can be designed to immediately start hashing once it has power. Most batch jobs need to boot up, load stuff into memory, do some work, save their results. This makes them much less flexible. Also I think electricity may not be the main cost in this case, though I'm less sure.)