How exactly does a 3-way switch work?

Question

I just finished replacing all of the switches and outlets in my apartment, after fighting a long war with a weird 3-way switch. Needless to say, I won, but I'm still trying to grasp the concept of how it works. I know how a single pole switch works, like so:

-->--HOT-WIRE-IN-->[/SWITCH/]-->--HOT-WIRE-OUT-->--

But how does a 3-way switch work? I know that we have 3 wires coming into the switch, 1) black hot in, 2) black hot out, and 3) red runner, but how does the switch actually work? What does it toggle? When I held up an electricity sensor to the wires, it seemed that wire 1 of course was always hot, but wire 2 and 3 were sometimes hot and sometimes not.

So, how does it actually work? What's being toggled and how?

Also, if you're wondering how to wire a 3-way switch, here's how: connect the black hot in wire to the only black screw, then connect the red runner wire to the brass screw on the same side as the black screw, and the hot out goes on the opposite side on the only brass screw. Just a tip :)

Answer 1

Here's a diagram. On the left the hot wire comes in and is switched to one of two wires going to the othe switch. The right switch selects eithe the on or off wire from the other switch. So either switch can be toggled to turn the light on or off.

Answer 2

Here's my latest evolution of my 3-way diagrams. I like this one because in your mind's eye, you can "slide" the light and switches left and right as needed to match your actual configuration.

I work in conduit and I actually do use these wire colors. It greatly improves clarity inside the junction box; otherwise 3-way boxes tend to be a spaghetti mess of black, white, red with color not indicating function. Someone working in cable can also get this benefit by marking wires with a 5-pack of colored tape.