An electrical engineer once told me that the key to understanding
electricity was that it always wanted to go directly to
ground, and it's willing to run our
washing machine in order to get there. Really all we do is make it jump through hoops on the way to power our computers, microwaves, and
iPods. That simple picture of a circuit as one wire that connects a power source to ground with a
light bulb in between is the first picture you need in your head when describing
knob and tube wiring.
Electricity was first identified in 1600 by William Gilbert but it was really nothing more than a curiosity until Thomas Edison started building devices like the aforementioned light bulb that could use electricity to get things done, and putting together power systems for houses and buildings. In the early 20th century the number of devices that existed to be powered was very small, and the primary purpose of electricity was lighting, which even then was far superior to candles or gas lighting. So early builders thought in terms of powering a few devices. Edison worked in direct current where the current quite literally flows in only one direction. So they thought simply. One wire up to a switch, to turn the light on or off by opening or closing the circuit (a closed switch passes electricity). One side came from a generator, and the other eventually terminated in the ground. So if you want to wire up a light in the kitchen as well as the living room, you just spilt the wire before the living room and reconnect it after. Wire runs paralleled each other, and while a house might have many circuits, they were run pretty much the same, like one way streets, with differing devices paralleling each other. In fact they had to run in parallel because if they didn't the first switch would kill everything on that circuit.
So the first thing you need to understand about knob and tube wiring, that it's run like a one way street. One that might have many individual lanes, but ultimately it only goes one way. Copper was pretty expensive back then,so it was cheaper to run single wires one way. It's also important to remember that drills were hand-powered back then, so running a single wire across joists required a lot of time (and therefore money).
But you still needed insulation. Electricity will take whatever path to ground it finds, and that includes you or the joists holding up your floor. Early cloth insulation was expensive and short lived, and rubber was pretty new as well. Neither were terribly durable at the time. Early on they discovered porcelain was an excellent insulator, in fact it's still used on transmission lines today. Porcelain is immune to aging. So when you wanted to pass through something you drilled a small hole, and inserted a porcelain tube for the wire to pass through. When the wire needed to change direction, early electricians wound it around a porcelain knob. Branches were soldered together. By those means wires could be run through your house. In fact, you technically need no other insulation provided the walls aren't stuffed with insulation.
Most houses built in the first half of the 20th century used knob and tube wiring. But we don't do that any more for a simple reason. Electricians like myself call the wire going out to the device the 'hot' and the path back to ground the 'neutral'. There are several reasons but trust me, the voltage coming back is a lot less than the volts going out. The difference in power and amps is the power consumed operating the appliance. The problem is that when an electrician looks at that wire, all he sees is a wire. Is it a hot? Or a neutral? No way to tell and for reasons of safety and convenience the distinction matters. Today the National Electric Code specifies (with a few clearly defined exceptions) that ungrounded (hot) and grounded (neutral) conductors shall be run together and the neutral shall be identified with a white or gray color. That bit of code makes it a lot easier for me to add an extra outlet for your home theater.
There is nothing inherently dangerous about knob and tube wiring, provided you leave it alone and respect the limits of the circuit. This means don't add anything and don't overload it. Don't up-size the fuse if it blows, unplug your hair dryer. Which we do not like to do. Electric appliances were rare and expensive in 1908. In 2008 they're everywhere. The only solution to more devices is more circuits (and maybe a larger electric service), and by code new circuits cannot be installed as knob and tube.
DonJaime tells me that Joseph Swan is the true inventor of the light bulb, and his writeup offers a reasonable argument for Swan. Of course, Edison had a lab about two hours drive from where I grew up, so I'll stick with Edison.
cbustapeck recently wondered why insurance companies are so down on knob and tube wiring, particularly when combined with a fusebox. There are a couple reasons. First of all, except for a few very high end homes most houses built with knob and tube wiring were designed with an expected load of a bunch of electric lights and maybe a radio in the living room. Think about the sort of appliances people used in 1930 and you'll get the idea. Those homes were run with very few circuits. If you tap them and add on then it's very easy to overload the circuit. It gets even worse with fuses. The h-type screw in fuses used are nice because they're easy to change, but no matter the rating they're all the same size. When a fuse blows, the first thing many people do is screw in a bigger fuse. Fuses are there to keep the circuit from providing more current then it can safely handle. The fuse size is matched to the size of the wire. So with a fuse box its very easy to screw in a fuse which will allow users to overload the circuit it's supposed to protect. Overloaded circuits get hot. Overloaded circuits start fires.
Imagine this scenario. Joe Homeowner wants some new outlets, and gets them added to an existing circuit. Only now he starts blowing fuses. So he upsizes the fuse! And maybe he gets away with it for a while. Then he wants to add another outlet for a new TV. And the fuse blows during the Super Bowl. So he stuffs in an even bigger fuse, and the wires just wont' take it any more. This is how insurance claims are born! Circuit breakers can also be changed, but the work requires tools, and breakers are often screwed directly into the busbbars carrying the current. As an electrician I can change them easily, but I also have training so I know why I can't replace that fifteen amp breaker with a thirty when it trips too often. I also know upsizing it makes me liable. The right solution is to run a new circuit, so that's what I'll tell you to do. Insurance companies spent years paying claims for fires started by people who upsized their fuses unknowingly, or even worse, replaced it with a penny. (Putting a penny ahead of a dead fuse is an old trick that removes ALL semblance of overcurrent protection from a circuit. Suffice to say, that if the insurance inspector finds a penny in your fusebox, your claim will be denied!) Therefore, they've seen a LOT of abuse and regard fuseboxes as risky, even though a properly sized fuse is more reliable then a breaker.