What is a channel in a CNN?
Let's assume that we are talking about 2D convolutions applied on images.

In a grayscale image, the data is a matrix of dimensions $w \times h$, where $w$ is the width of the image and $h$ is its height. In a color image, we normally have 3 channels: red, green and blue; this way, a color image can be represented as a matrix of dimensions $w \times h \times c$, where $c$ is the number of channels, that is, 3.

A convolution layer receives the image ($w \times h \times c$) as input, and generates as output an activation map of dimensions $w' \times h' \times c'$. The number of input channels in the convolution is $c$, while the number of output channels is $c'$. The filter for such a convolution is a tensor of dimensions $f \times f \times c \times c'$, where $f$ is the filter size (normally 3 or 5).

This way, the number of channels is the depth of the matrices involved in the convolutions. Also, a convolution operation defines the variation in such depth by specifying input and output channels.

These explanations are directly extrapolable to 1D signals or 3D signals, but the analogy with image channels made it more appropriate to use 2D signals in the example.