Eigenclasses are used to implement Singleton Classes in Ruby. They are lightweight classes, created automatically for every object when methods are defined on that object. These Eigenclasses store the unique methods for the respective object.

When a singleton method is created, Ruby automatically creates an anonymous class to store that method. These anonymous classes are called metaclasses, also known as singleton classes or eigenclasses. The singleton method is associated with the metaclass which, in turn, is associated with the object on which the singleton method was defined.

In Ruby, all methods exist within a class. When you create an object, the methods for that object exist within it’s class. Methods can be public, private or protected, but there is no concept of a static method. Instead, we have singleton classes, commonly referred to as eigenclasses.