Effects package helps to manage additional program effects.
An Elm application (program/system) can be designed as a combination of sub-systems. Examples of sub-systems can be a system for animation, a system for communication with JS, a system for working with time, etc... Different sub-systems can communicate with each other using effects.
One of the concepts in Elm to maintain shared state is called "taco technique". Effects is a good way to update shared state because multiple effects can be processed at once.
Effects can be used together with elm-program-test package.
Please share what use cases you have.