Points rule labels allow you to specify how the rule looks like to customers on the frontend. This is usually used for Point Spending Rules to give a visual interface for rules that have an option of whether or not to be enabled.
The label is not used if you are using a points-only rule
You can set a default label to represent all labels, and/or you can specify store view specific labels that are different depending on the store view. Store view specific labels can be used for multi-language stores, customer naming per website, etc.