The display represents a map of space around the black hole in much the same that an ordinary map represents a portion of the surface of the Earth. Well-known distortions occur when the the curved 2-dimensional surface of the Earth is projected onto an ordinary flat 2-dimensional map. Similar distortions occur when the the curved space around a black hole is projected onto an ordinary flat 2-dimensional computer display screen. For the Earth, we are lucky that we can look at a globe if we want to to see a true representation of the surface of the Earth. Human beings cannot directly visualize the curved space around a black hole, and so have make do with maps like the one used by this animation.
To understand the motion on the display, first consider a car that starts in Toronto, drives to Montreal, travels to New York City, and finally returns to Toronto. This trip can be represented on an ordinary map by a closed path. A white dot that moves on the map as the car moves on the actual surface of the Earth might give a better representation of the trip. The animation applies this idea to the motion of a particle near a black hole. A white dot moves on the display map of space as a particle would actually move near a black hole, with the position of the dot on the map determined by the time on the particle's wristwatch.