When you live in a rural area, you often have to provide your own water by having a well and a septic tank. Modern wells require an electric pump to bring the water to the surface then push it through the plumbing in the house, all the way to the toilets. That is what we have.
No electricity = no push. No push = no flush*.
PS: We do keep gallon containers of water in each bathroom for use to emergency refill toilet tanks during times when electric service is likely to be disrupted and the need is great..
PS 2: We do have an emergency generator, but it is not automatic and requires a long cable to be plugged into the meter box. I will not stand in a 3 foot snowdrift or in a driving rain and open up that meter box cover to plug in that cable. Chicken Little here.
PS 3: Because I am still stuck in bed without being able to walk very far or use my hands for more than a few minutes at a time (Read: my wife would have to plug in the cable and pull start the generator by herself and that is not a pleasant thing) connecting the generator to the house is an option we have so far avoided. God bless the NorthWest Electric Coop for doing the fantastic job they do in keeping my power outages to a minimum.
* = Actually, there is one flush available during a power outage. It is the refill of the tank, after making that flush, that does not happen without electricity or manual refill.