Also: factory town, mill town, mining town, unincorporated town
A factory town is a town where a factory or industry dominates, maybe even owns, the town. The type of factory can vary from region to region. In the South you see a lot of textile mill towns. In West Virginia there are a lot of mining towns. Flint, Michigan used to be a car manufacturing town.
In a factory town, most people work for the factory or in a job dependant on the factory and as a result pretty much the worst thing that can happen is the closing of the factory. (Go watch Michael Moore's movies Roger and Me and The Big One for a great discussion of this)
(The following is mainly based on my knowledge of Southern mill towns. Your milage may vary in other cases)
Before the labor movement it was quite common for a factory to literally own a town. Look at a map of the south and you'll see Carrboro (named for the Carr Textile Mill), Kannapolis (Cannon Mills), Pelzer (Pelzer Manufacturing Co) and countless others.
Someone who wanted a factory would buy a big hunk of land and build a factory there. Then they would build houses, a church, a company store, a few roads, a medical clinic, and (if it was a nicer factory town) a school. If you worked for the factory (and if you lived in the town you pretty much worked for the factory) you lived in company housing, bought your goods at the company store, sent your kids to the company run school (which you can bet taught a very limited curriculum, mainly about how to be a good factory worker), and attended the company sanctioned church on Sundays (which you can bet had a lot of sermons about the good servant and the salvation of hard work).
Because these towns were often unincorporated (which I guess just kind of means "unofficial") they usually didn't have any kind of democratically elected town officials, a municipal police department, or public utilities. The leaders were the company owners, the police were the company security guards and if you had running water or electricity (though you probably didn't in the pre-WWII rural South) you bought it from the company.
Post-labor movement, a lot of things have changed (child labor laws, tenant's rights, 8-hour days & weekends off) but probably not as much has changed as you'd think.
This is what a Southern mill town looks like:
The town is probably named after a factory or the owner of a factory. Maybe the factory is still open, maybe not. Maybe it has been turned into a mall. The factory is big. Really big. Probably the biggest building in the town. It is probably brick, definitely imposing, and sometimes looks like a church. Look for machine-gun turrets on the top (to shoot workers who tried to walk out on strike).
Next to the factory (which is probably near the center of town) look for the shopping district and the historic district. There are some very nice homes here, probably well maintained and expensive looking. This is where the factory owner, his relatives, and management used to live (and often still do live).
A few streets down you'll find smaller houses that all look the same. Maybe duplexes. We call them "mill houses" and actually, I quite like them. They are very in style these days, especially with young couples buying their first homes, who don't mind how small they are. This is where lower management, technicians, and the more established factory workers used to live (and often still do live).
As you get farther and farther away from the factory you'll find smaller and more run down houses, until finally you get to the trailer park. (This is where the shanty town used to be.)
Once a history teacher pointed out this pattern to me (in the town I had lived in my whole life, I had never noticed it) I started seeing it everywhere in the south. Next time you're in a small town, look around at the layout. It can tell you a lot about where the town came from.