This is detailed with a reasonable amount of detail by Guido himself in his blog post Method Resolution Order (including two earlier attempts).

In your example, Third() will call First.__init__. Python looks for each attribute in the class’s parents as they are listed left to right. In this case, we are looking for __init__. So, if you define

class Third(First, Second):
    ...

Python will start by looking at First, and, if First doesn’t have the attribute, then it will look at Second.

This situation becomes more complex when inheritance starts crossing paths (for example if First inherited from Second). Read the link above for more details, but, in a nutshell, Python will try to maintain the order in which each class appears on the inheritance list, starting with the child class itself.

So, for instance, if you had:

class First(object):
    def __init__(self):
        print "first"

class Second(First):
    def __init__(self):
        print "second"

class Third(First):
    def __init__(self):
        print "third"

class Fourth(Second, Third):
    def __init__(self):
        super(Fourth, self).__init__()
        print "that's it"

the MRO would be [Fourth, Second, Third, First].

By the way: if Python cannot find a coherent method resolution order, it’ll raise an exception, instead of falling back to behavior which might surprise the user.

Example of an ambiguous MRO:

class First(object):
    def __init__(self):
        print "first"
        
class Second(First):
    def __init__(self):
        print "second"

class Third(First, Second):
    def __init__(self):
        print "third"

Should Third‘s MRO be [First, Second] or [Second, First]? There’s no obvious expectation, and Python will raise an error:

TypeError: Error when calling the metaclass bases
    Cannot create a consistent method resolution order (MRO) for bases Second, First

Why do the examples above lack super() calls? The point of the examples is to show how the MRO is constructed. They are not intended to print "first\nsecond\third" or whatever. You can – and should, of course, play around with the example, add super() calls, see what happens, and gain a deeper understanding of Python’s inheritance model. But my goal here is to keep it simple and show how the MRO is built. And it is built as I explained:

>>> Fourth.__mro__
(<class '__main__.Fourth'>,
 <class '__main__.Second'>, <class '__main__.Third'>,
 <class '__main__.First'>,
 <type 'object'>)