x.instance_eval changes your context so self evaluates to x.
This allows you to do many things, including defining instance variables and instance methods but only for x.
 x = Object.new
 y = Object.new
 # define instance variables for x and y
 x.instance_eval { @var = 1 }
 y.instance_eval { @var = 2 }
 # define an instance method for all Objects
 class Object
   def var
     @var
   end
 end
 x.var #=> 1
 y.var #=> 2
Ruby lets you define instance methods for an object in a couple places.  Normally,
one defines them in a class, and those instance methods are shared among all instances
of that class (like def var above).
However, we can also define an instance method for just a single object:
# here's one way to do it
def x.foo
  "foo!"
end
# here's another
x.instance_eval do
  # remember, in here self is x, so bar is attached to x.
  def bar
    "bar!"
  end
end
Even though x and y have the same class, they don't share these methods, since they were only defined for x.
x.foo #=> "foo!"
x.bar #=> "bar!"
y.foo #=> raises NoMethodError
y.bar #=> raises NoMethodError
Now in ruby, everything's an object, even classes.  Class methods are just instance methods
for that class object.
# we have two ways of creating a class:
class A 
end
# the former is just syntatic sugar for the latter
B = Class.new
# we have do ways of defining class methods:
# the first two are the same as for any other object
def A.baz
  "baz!"
end
A.instance_eval do
   def frog
     "frog!"
   end
end
# the others are in the class context, which is slightly different
class A
  def self.marco
    "polo!"
  end
  # since A == self in here, this is the same as the last one.
  def A.red_light
    "green light!"
  end
  # unlike instance_eval, class context is special in that methods that
  # aren't attached to a specific object are taken as instance methods for instances
  # of the class
  def example
     "I'm an instance of A, not A itself"
  end
end
# class_eval opens up the class context in the same way
A.class_eval do
  def self.telegram
    "not a land shark"
  end
end
Note again, that all these methods are A-specific, B doesn't get access to any of them:
A.baz #=> "baz!"
B.telegram #=> raises NoMethodError
The important thing to take away from here is that
class methods are just instance methods of an object of class Class