Electricity comes to your home via a very complex grid but for the sake of simplicity we'll start with the 2400v to 16,000v (called line or primary voltage) distribution voltages common in rural and suburban Canada. (there are lots of other voltages and systems, but this is typical).
The primary is stepped down through the transformer (pole or pad mounted) to the 120/240v used in the home.
When the power goes out the automatic transfer switch opens the line side of your household main and closes another switch that is wired to your genie and whatever you are going to power up. A manual switch does the same thing, only is operated...manually.
We'll use the dryer plug example, but this basically applies to all the hack-rigged jobs. By the by a dryer plug is generally only rated to a max of 40 amps, it won't power everything in your house. When the dryer plug set up is powered up with the generator the 120/240v that is now partially powering your home also goes through the main switch (because the homeowner forgot or just plain didn't know to open it, even with it open, the neutral connections are still there, thank you Gerald) and out to that transformer that feeds you and your neighbours. Distribution transformers are both step-up and step-down. That means the household voltage is now feeding the can and primary voltage (remember the 2400v to 16000v) is now coming out and it travels a long, long way.
So those lines that are laying on the ground in the storm can now be live and stumbled across by any one. The line crew down the way is out to do repairs and is unaware of the illegally wired generator (they have killed before). Partial voltage or "brown out" type voltages are feeding homes and causing damage to any kind of household equipment. (see my previous post for what does happen when the line crew snaps a set of grounds on this type of set up)
