Early video games systems had limited graphics capability. To get around this limitation game developers would come up with a solution still used today.
They used sprites, 2D bitmap graphics, to depict movement. Sprites are a sequence of images that the game system would show to create the illusion of movement. To make characters run, the system would move the picture along the x axis of the screen. One of the most iconic early uses of this technology is in Pac-Man.
The development of this animations often relies on sprite sheets. Which are a convenient way for packing sprites into a single file. Creation of sprite animations is often a labour of love. Animators spend hours making sure image fits well with the image before and after. Today sprite animations are expressions of dedication to game feel.