Solution 1:

First, the class << foo syntax opens up foo's singleton class (eigenclass). This allows you to specialise the behaviour of methods called on that specific object.

a = 'foo'
class << a
  def inspect
    '"bar"'
  end
end
a.inspect   # => "bar"

a = 'foo'   # new object, new singleton class
a.inspect   # => "foo"

Now, to answer the question: class << self opens up self's singleton class, so that methods can be redefined for the current self object (which inside a class or module body is the class or module itself). Usually, this is used to define class/module ("static") methods:

class String
  class << self
    def value_of obj
      obj.to_s
    end
  end
end

String.value_of 42   # => "42"

This can also be written as a shorthand:

class String
  def self.value_of obj
    obj.to_s
  end
end

Or even shorter:

def String.value_of obj
  obj.to_s
end

When inside a function definition, self refers to the object the function is being called with. In this case, class << self opens the singleton class for that object; one use of that is to implement a poor man's state machine:

class StateMachineExample
  def process obj
    process_hook obj
  end

private
  def process_state_1 obj
    # ...
    class << self
      alias process_hook process_state_2
    end
  end

  def process_state_2 obj
    # ...
    class << self
      alias process_hook process_state_1
    end
  end

  # Set up initial state
  alias process_hook process_state_1
end

So, in the example above, each instance of StateMachineExample has process_hook aliased to process_state_1, but note how in the latter, it can redefine process_hook (for self only, not affecting other StateMachineExample instances) to process_state_2. So, each time a caller calls the process method (which calls the redefinable process_hook), the behaviour changes depending on what state it's in.

Solution 2:

I found a super simple explanation about class << self , Eigenclass and different type of methods.

In Ruby, there are three types of methods that can be applied to a class:

  1. Instance methods
  2. Singleton methods
  3. Class methods

Instance methods and class methods are almost similar to their homonymous in other programming languages.

class Foo  
  def an_instance_method  
    puts "I am an instance method"  
  end  
  def self.a_class_method  
    puts "I am a class method"  
  end  
end

foo = Foo.new

def foo.a_singleton_method
  puts "I am a singletone method"
end

Another way of accessing an Eigenclass(which includes singleton methods) is with the following syntax (class <<):

foo = Foo.new

class << foo
  def a_singleton_method
    puts "I am a singleton method"
  end
end

now you can define a singleton method for self which is the class Foo itself in this context:

class Foo
  class << self
    def a_singleton_and_class_method
      puts "I am a singleton method for self and a class method for Foo"
    end
  end
end

Solution 3:

Usually, instance methods are global methods. That means they are available in all instances of the class on which they were defined. In contrast, a singleton method is implemented on a single object.

Ruby stores methods in classes and all methods must be associated with a class. The object on which a singleton method is defined is not a class (it is an instance of a class). If only classes can store methods, how can an object store a singleton method? 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.

If multiple singleton methods are defined within a single object, they are all stored in the same metaclass.

class Zen
end

z1 = Zen.new
z2 = Zen.new

class << z1
  def say_hello
    puts "Hello!"
  end
end

z1.say_hello    # Output: Hello!
z2.say_hello    # Output: NoMethodError: undefined method `say_hello'…

In the above example, class << z1 changes the current self to point to the metaclass of the z1 object; then, it defines the say_hello method within the metaclass.

Classes are also objects (instances of the built-in class called Class). Class methods are nothing more than singleton methods associated with a class object.

class Zabuton
  class << self
    def stuff
      puts "Stuffing zabuton…"
    end
  end
end

All objects may have metaclasses. That means classes can also have metaclasses. In the above example, class << self modifies self so it points to the metaclass of the Zabuton class. When a method is defined without an explicit receiver (the class/object on which the method will be defined), it is implicitly defined within the current scope, that is, the current value of self. Hence, the stuff method is defined within the metaclass of the Zabuton class. The above example is just another way to define a class method. IMHO, it's better to use the def self.my_new_clas_method syntax to define class methods, as it makes the code easier to understand. The above example was included so we understand what's happening when we come across the class << self syntax.

Additional info can be found at this post about Ruby Classes.