The power company has protective devices, kinda along the same lines as the breakers in your house. If there’s a fault, the protective devices shut the line off, just like the breakers in your house do. In your home, you remove the fault that tripped the breaker (maybe you had too many things plugged in and blew it) then you go down to the basement or wherever your box is located and you flip the breaker back on.
The problem with the power company is that its “breakers” are spread out all throughout its service area, so having someone do the equivalent of flipping the breaker back on means someone needs to get into the truck and drive quite a distance. It takes them a lot longer to flip the breaker back on. What makes it even worse is that the power company’s faults are usually transitory, like a tree limb blows over and hits a line causing a short. A second later, the tree limb is back out of the way, but the line still tripped.
Just so that you’re not out of power for a really long time every time this happens, the power company uses these things called automatic reclosers, which you can think of as breakers that automatically flip themselves back on. The reclosers are programmable so they can be set any way that the power company wants to set them, but usually they turn the line back on a couple of times fairly quickly (like one and two seconds after the fault) and then once more after a longer period of time has passed (say, two minutes). If the line stays on after it flips the power back on, then everything is fine If the line keeps faulting then the recloser gives up after its last retry and at that point then someone does have to get in the truck and go find out what went wrong and fix it. Since most faults are transitory, the automatic reclosers prevent the power going out for extended periods of time. If a power line blows into branches or a branch blows into the line, or a squirrel or some other critter accidentally shorts himself out at a transformer (happens more often than you might think) then the power blinks off for a second, then comes back on when the recloser restarts the line.
This is one of many reasons to stay away from downed power lines. The line may have tripped and may be dead at the moment, you go over and touch it and you’re fine, then the recloser pops on and you get zapped and killed. Also, just because the line fell down doesn’t necessarily mean that the line tripped. It may still be live.
Many power distribution lines can also be fed from different substations, so if something fails on one end they can switch over to feeding it from the other end. This can often restore power to most, if not all, of the customers fed by that line and it allows the power company to isolate the fault to a smaller number of homes fairly quickly.
And there’s the issues that previous posters have mentioned. There’s a thing called a “cascade failure” which is really bad and you try to avoid it. Let’s say for example you have five areas, which we’ll call A, B, C, D, and E. There are generators in B and E which share feeding power to all five areas. There’s a fault in A which overloads the generator in B and causes it to shut down. A and B are now without power. The generator in E can’t supply enough power for the remaining sections, so it trips, shutting down power to C, D, and E. Everyone goes dark, because of a single fault in A. To prevent this from happening, you need really fast fault detectors that can shut off A before the failure cascades to other areas. Cascade failures occur more often when systems are extremely heavily loaded, which is the northeast and southwest U.S. every summer when everyone has their air conditioners on. In 2003 for example, a cascade failure started with a line in Ohio that sagged in the heat and shorted out against branches, and ended up taking out power in most of the northeast as well as parts of Canada. To prevent cascade failures, they often shut off or reduce power (brownout) to certain overloaded areas to prevent them from tripping the entire system, as gotpasswords mentioned. If you are in one of the affected areas, your power might be shut off completely, or you might experience a brief momentary power outage as your area is switched from one feed to another to prevent it from getting overloaded.
I can’t tell which of these your power company is referring to on your bill.