Once any particle is generated by an emitter, its motion is governed by forces. By default this is gravity, provided by the Particle Simulation item. While Dynamics Forces and falloffs can produce interesting effects, it is the particle operators that give you broad control over Particles in motion, providing effects for age, speed, collision and a multitude of other controllers. Flocking controls how particles move relative to its neighbors, dynamic fluid allows particles to cling closely together, simulating viscous fluids, while terminators cause particles to die within the bounds of a falloff. Really, operators can be seen as part of the building blocks that can be added to an overall simulation to provide a huge number of possibilities.