Its a fuel cell, it combines fuel and oxygen chemically to create electric power. Wikapedia has an article explaining fuel cells
http://en.wikipedia.org/wiki/Fuel_cell
There is no combustion of any kind in the unit. The major improvement is that prior fuel cells usually required very expensive catalysts and the membranes were hard to make. If they have come up with a cheap to make membrane with no expensive catalysts, that drops the price down. Most prior fuel cell membranes are very prone to "poisoning" by various impurities in the fuel, if the Bloom design is less affected by contaminants thats an improvement . Wood Gas is pretty complex and had a lot of contaminants so I dont see it being used in a fuel cell for awhile.
A fuel cell still requires fuel, in this case natural gas. It still generates CO2 and therefore isnt renewable. It is claimed to be more efficient at converting natural gas to electricity than an internal combustion engine so it produces less CO2 per KW generated and that also is a good thing if you need electricity rather than heat. If you want to heat your house, its not a plus. I see a sterling cycle generator being a lot better fit (and a lot less complex) for generating power from wood.
I will point out that the comparison of solar cells to a fuel cell unit was "apples to oranges", once the solar cells are installed they generate power for 20 plus years with zero fuel and zero carbon emmisions after the initial CO emisions are covered for fabricating the PV panels (typically 18 months of generation). A 100KW unit at $800,000 is roughly on par with solar electric generated power (typical range per installed KW for commercial installation for solar is 7 to 9 dollars per watt or $700,000 to $900,000 for an equivalent PV array with the potential to drop down to 4 to 5 dollars per watt). Granted the Bloom unit takes up a lot less space, but its burning fuel whenever its running. The reason the current users save money with it instead of grid power is that is subsidized by other rate payers. California basically requires the utilities to buy all renewable power generated and pay a premium which is subsidized by the rate payer. As more renewable goes on line, the electric costs for the average rate payer goes up making renewable more attractive. Note that in the long run it starts to resemble a Ponzi scheme. If someone runs the numbers they will find that the natural gas cost starts to be the big cost to run the unit even if the initial cost of the unit drops.
Fuel cells have traditionally been very difficult to throttle, they want to run steady state, I expect that if they come up with a home version, it will be grid tied so that it can run at one speed and send the power out to the grid. I dont see a home unit being a good standby generator when the grid is down unless the house has a battery bank to provide the steady load.
The script from the CBS show was very similiar to a story several years ago on Ballard Power Systems about a fuel cell vehicle, plus a big show on how Segways were going to change the world, or Dean Kamens wheelchairs that could stand upright were going to change the world and a couple of other shows on "the next best thing" that havent happened yet. It makes for great TV, but a lot of "the next best things" dont pan out as quickly and as cheaply as represented.
More power to Bloom for advancing the state of the art and I expect that they will find a market for the product and plenty of folks who want to buy shares in the company. With the amount of capital they have sunk into it, they have some significant debts to the venture capitalists who funded it up front that they will have to pay off and thats going to keep the equipment price high for several years.