C# new and override

I am pretty new to C# (and anything really other than web languages). I am trying to understand two keywords in C# dealing with polymorphism. Can you please tell me if the following is correct?

New keyword – just states that there is a method in the child class with the same name as one in the base class, prevents an error. Hides the child method from the parent method.
Override keyword - Child method that actually overrides the method of the same name in the parent class.

If the new keyword as I stated is correct, why would you ever even create a method with the same name within a child class. Wouldn't it always be over-written by the parent?

re: C# new and override

"the new keyword explicitly hides a member inherited from a base class. Hiding an inherited member means that the derived version of the member replaces the base-class version." (C# Lang Ref)

"Hides the child method from the parent method" is probably not precise.

The child method replaces the parent method entirely. The inheritance chain is stopped. In a certain sense, the parent method is now "hidden" to you child class.

A contrived example based on something I came across once is setting a static value (note: this is not good design, just an example):
All my derived classes would share that StartValue. If I change it in one class:

it is now changed for all my classes.

However, if for one derived class I declare
it is now changed just for DadsCheckingAccount without affecting other CheckingAccount derived classes.