What does def `self.function` name mean?

In ruby self is somewhat similar to this in java, but when it comes to classes its more like the keyword static in java. A short example:

class A 
  # class method 
  def self.c_method
    true
  end
  # instance method
  def i_method
    true
  end
end

A.c_method #=> true
A.i_method #=> failure
A.new.i_method #=> true
A.new.c_method #=> failure

Update: Difference between static methods in java and class methods in ruby

Static methods in Java have two distinct features that makes them different from instance methods: a) they are static, b) they are not associated with an instance. (IOW: they really aren't like methods at all, they are just procedures.) In Ruby, all methods are dynamic, and all methods are associated with an instance. In fact, unlike Java where there are three different kinds of "methods" (instance methods, static methods and constructors), there is only one kind of method in Ruby: instance methods. So, no: static methods in Java are completely unlike methods in Ruby. – Jörg W Mittag 1 hour ago

Contrary to other languages, Ruby has no class methods, but it has singleton methods attached to a particular object.

cat = String.new("cat")
def cat.speak
    'miaow'
end
cat.speak #=> "miaow" 
cat.singleton_methods #=> ["speak"] 

def cat.speak creates a singleton method attached to the object cat.

When you write class A, it is equivalent to A = Class.new :

A = Class.new
def A.speak
    "I'm class A"
end
A.speak #=> "I'm class A" 
A.singleton_methods #=> ["speak"] 

def A.speak creates a singleton method attached to the object A. We call it a class method of class A.

When you write

class A
    def self.c_method
        'in A#c_method'
    end
end

you create an instance of Class(*). Inside the class definition, Ruby sets self to this new instance of Class, which has been assigned to the constant A. Thus def self.c_method is equivalent to def cat.speak, that is to say you define a singleton method attached to the object self, which is currently the class A.

Now the class A has two singleton methods, that we commonly call class methods.

A.singleton_methods
 => ["c_method", "speak"] 

(*) technically, in this case where A has already been created by A = Class.new, class A reopens the existing class. That's why we have two singleton methods at the end. But in the usual case where it is the first definition of a class, it means Class.new.