Note: This tutorial is intended for beginners. It explains some basics, but it does get pretty deep into Photoshops innards here and there. If you believe anything is incorrect here, then please me, I'm always learning myself. Also keep in mind things are being extremely simplified because the details of Photoshop's innards scare me.
This tutorial is intended to give a quick overview of how Photoshop sees and interprets Channels, as well an an in-depth explanation of what Channels actually are.
It can be assumed that most people reading this know that Photoshop is a bitmap program, and that bitmap pictures are composed of a whole pile of little dots called pixels. But, what many Photoshop users don't know is that while they are creating ultra colorful pieces of art, photoshop is, in a way, color blind.
What does this mean? Well, to explain that, we need to talk about Color Modes and Color Separation and Channels.
Remember physics class? Remember learning about the light spectrum? The Human Eye can see only a small band of visible light among microwaves, radiowaves, etc, etc? Well, just because it's virtual doesn't mean physics stops working. Photoshop uses a small section of the visible light to display its colors, and different sections of the spectrum, called Gamuts, are labeled as different Color Modes. The most common Color Mode for print pieces (files outputed through a printer) is CMYK. This means that every color in the Gamut that makes up all the files' colors are mixed from Cyan, Magenta, Yellow, or blacK. Almost all printers use this four color process.
Sidenote: RGB (Red, Green, Blue) is the Color Mode for the web and anything that is only viewed on a monitor. RGB printers do exist, but they cost a boatload of money. It is interesting to note that the RGB Gamut is larger than the CMYK Gamut, meaning that it includes more of the visible spectrum and therefor, more colors. Soooo, if you start working on a picture in RGB, there's a good chance your colors may not translate correctly to CMYK, because it won't exist in that Gamut. This is where you start getting into the wonderful land of Color Correction, which is poopy, so I won't talk about it.
Don't worry, I'm getting to the black and white part, and to the tutorial part. If you ever contract a professional printer than they will take your file and pull apart all the colors, each into their own color plate. This is called Color Separation. Printers take a file and all the Cyan colors they put on one plate, all the Yellow colors they put on another plate and so forth. Each plate is in grayscale, with light areas signifying where that color ink is placed on the page, and darker signifying where it is omitted. To sum this up, the Printer drops ink over the page four times, one for each plate, and the colors are mixed magically on the paper!
Now, behind the scenes, Photoshop is working the same way. If you are working in RGB mode, for example, Photoshop separates the colors out into three plates, called Channels in Photoshop; a red channel, a green channel, and a blue channel. If you open the channel pallete you can see these three channels, all represented in black and white. And to the user's eye, Photoshop magically mixes the colors on screen.
Side note: Just because there are 3 channels by default for RGB Color Mode, and 4 for CMYK, doesn't mean that you are only limited to having 3 channels. Additional channels don't necessarily alter the color in the image though, and instead are used for other purposes. For example, channels are an excellent way to store selections.
Here's a handy experiment to show off this process.
Start with a normal RGB image and fill it with black. Now, go to windows>show channels if the channels palette isn't already open. Click on just the red channel and use the paintbrush to draw a white circle on it. While you paint in white on the Red channel, you can see the RGB channel update with a red circle
Click on the Green Channel and draw another pure white circle, this one partially overlapping old one. The red circle will disappear when you first click on the green channel, since red is invisible on that channel, but if you click just on the little "eyeball" icon box next to the red channel you can view it. Don't click on the channel itself though, or you'll be painting on the wrong channel.
Click on the RGB channel, which displays all channels at once, and you can see where the green and red circle overlap there is Yellow.
If you feel creative, draw on the blue channel with white, overlapping both other circles and you can mix a pure white in the center!
Anyway. To sum all this up in one, over simplified sentence, A Photoshop file is not just a collection of pixels. A Photoshop file is an arrangement of pixel data, each holding an address as to placement in the file and a value of grayness for each and every channel in it's color mode.
Learn how to use channels to your advantage. Just like with everything in Photoshop you can select, manipulate, distort and tweak them to tailor to your needs. Try running filters on just one channel of a photo, it's fun!