Think a minute of what a motion blur means for the physical pixels: they are moved during the acquisition process.
Assuming left-to-right horizontal motion for simplicity, then what happens is that one pixel will measure the amount of light in its initial position, then the light in the position that was occupied before by its right neighbour, and so on until the frame acquisition ends.
Mathematically, the light measured by one pixel is then a mixture between the value in its original position and the values of its neighbours in their original positions.
Hence, up to a rescaling of the output value (that is unnecessary of you normalize the blur kernel), an horizontal motion blur can be modelled by an horizontal blur kernel.
Of course, this is grossly simplified (I did intentionally forgot about minimum exposure time for example and supposed instead that the measurement was instantaneous) that assumes that the scene is at a fixed distance from the camera and that all the image points are at the same distance, without independantly moving objects.