How does the quality of my code gets affected if I don't use __init__ method in python? A simple example would be appreciated.
Its not a matter of quality here, in Object-oriented-design which python supports, __init__ is way to supply data when an object is created first. In OOPS, this is called a constructor. In other words A constructor is a method which prepares a valid object.
There are design patters on large projects are build that rely on the constructor feature provided by python. Without this they will not function,  
for e.g.

You want to keep track of every object that is created for a class, now you need a method which is executed every time a object is created, hence the constructor.      
Other useful example for a constructor is lets say you want to create a customer object for a Bank. Now a customer for a bank will must have an account number, so basically you have to set a rule for a valid customer object for a Bank hence the constructor.
What happens when your class does not explicitly define an __init__ method?