A ComponentSystem in Unity (also known as a system in standard ECS terms) performs operations on entities. A ComponentSystem cannot contain instance data. To put this in terms of the old Unity system, this is somewhat similar to an old Component class, but one that only contains methods. One ComponentSystem is responsible for updating all Entities with a matching set of components (that is defined within a struct called a ComponentGroup).
Unity ECS provides an abstract class called ComponentSystem that you can extend in your code.
See also: System update order.