Here is a video of the particle effect in action. On the right, you can see a drop-down for “movement.” This is basically because some effects are designed to be watched “in motion” (e.g. the smoke trails behind a missile) while some are designed to be watched in one place (e.g. the explosion). The “random” movement you can see I’ve got selected just moves the effect to a random location each time I click “reset” (clicking “reset” obviously restarts the effect from the beginning).

Just because some people may not want to watch the video, here’s a screenshot of the particle effect viewer. Of course, a screenshot of a particle effect does not do it any sort of justice!