Signal is something that carries information. Usually, something is a pattern of variations of physical quantity that can be manipulated, stored, or transmitted by a physical processes. I am wondering that how image can be a signal. Ok, it is stored, manipulated, transmitted digitally, but how it can carry variations? Also how video can be kind of a signal?
A signal doesn't have to be a single quantity; the variation doesn't have to happen along a single axis, either.
An image is information (e.g. brightness) varying in two dimension (e.g. along a X- and a Y-axis).
Simple as that; counts both for digital and analog images.
That information that changes might be one-dimensional (e.g. only brightness for a black and white / grayscale image), or multidimensional (e.g. red, green, blue for a color picture).
Video is information varying in three dimensions: two dimensions like an image, and time as third dimension.
To build on Marcus's answer, when we have multidimensional data (e.g., stereo audio, video images), we often want to transform it into a one-dimensional signal so that we can transmit it over a single wire or as a radio signal.
There are many ways to do this. For example, with stereo audio, we translate one of the channels1 to a different range of frequencies and then add it to the other channel. This creates a single signal that can be transmitted and then decoded to produce the original two channels of audio. The general term for this is "frequency-division multiplexing".
For video, we take a different approach. We sample the pixel data in time, and then serialize all of that data (i.e., send pixels one at a time) into a high-bandwidth channel, combining the data with synchronization signals that allow us to keep track of where each data item belongs in the image. Again, this one-dimensional signal can be transmitted over a wire or over the air. The general term for this is "time-division multiplexing".
1 I'm ignoring the details of sum and difference processing for simplicity.