What does "channel" mean in digital photography?

In the context of a digital image, a channel is simply an array of values, one per pixel, that together specify one aspect or dimension of the image. For example, you can describe an image by specifying the red, green, and blue values for each of the pixels in the image. This is known as RGB (for red, green, blue). An RGB image has three channels. The red channel is an array of values that specifies the intensity of red for each pixel in the image. The green and blue channels similarly specify the intensity of green and blue, respectively, for each pixel. When the three channels are combined, you get a full color image.

So, let say we've got a photo of a duck. As I said above, any given channel represents only one component of the image information, so we can visualize a channel as a grayscale image by interpreting the channel as indicating intensity. Here's what the red channel looks like:

Because this is the red channel, a white pixel in this image means that the pixel will have the maximum amount of red in the final photo. A black pixel has zero intensity, so there will be no red in the corresponding pixel in the final image. Here are the green and blue channels:

When the channels are interpreted together as red, green, and blue you get the full color image:

There are other color models beside RGB, such as the HSV (hue, saturation, value) and CMYK (cyan, magenta, yellow, black) models. These also use channels to represent the various components of each pixel. And channels can be used to represent other kinds of per-pixel information, too. For example, RGBA images are just like the RGB image above, except that they have a fourth channel that indicates the alpha or transparency value for each pixel.