Each point represents a real asteroid. More asteroids become visible as the timeline reaches the date that they were first observed, starting with Ceres in 1801.
Orbital positions are calculated every frame by approximately solving Kepler's Equation on the GPU.
Depending upon the oomph of your machine, displaying less asteroids may be preferable. This can be chosen by passing the desired max number of asteroids as a url parameter:
10,000 Asteroids | 50,000 Asteroids | 200,000 Asteroids | 688,804 Asteroids