A rule is used to define behaviours for your particles.
There is two type of rules: event based and continuous.
They can be used, for example, to emit a trail of particles behind some other particles. They can also be used to explode a particle into hundreds of others, with different colors and behaviours themselves.
Rules can also be used to define the physics of a particle, to make it bounce off objects in the scene, or to destroy it upon impact.
A very important concept in particles rules is the particle's Group. When created, a particle is in the Group [1]. You can increase that Group ID using a Change Group Set or increase the Group ID of a particle Read More (in case of the Emit Emit a number of particles from another particle Read More , a Change Group Set or increase the Group ID of a particle Read More will automatically be added to increase the particles Group ID).
If you want to make a particle split once, when hitting a surface, the rule should be applied only on the first Group. Then, you should increase the Group when splitting to ensure it doesn't happen again.

Here is a little schematic:


Here is some tutorials to help you get the particle rules concept :

Go see the Group 3d Mask Mask according to object id or particles group Read More part of the documentations for further details on particles Groups.