Inheritance is a type of class or object association. The concept of a class makes it possible to define subclasses that share some or all of the main class characteristics. This is called inheritance. Inheritance also allows you to reuse code more efficiently.
Designing with Inheritance
In a class tree, inheritance is used to design classes vertically. (You can use Interfaces to design classes horizontally within a class tree.) With inheritance, you are defining an "is-a" relationship (i.e. a chow is-a dog). Analysts using UML call this generalization where you generalize specific classes into general parent classes or take general parent classes and specialize them as needed in child classes.
Inheritance is Generalization
Inheritance is Generalization and the terms can almost be used synonymously. In general, I prefer to use the term generalization when talking to analysts trying to understand a problem domain and inheritance when talking to programmers who need to implement an OOP solution.
A.k.a. Overriding, Inclusion Polymorphism, Runtime Polymorphism, Dynamic Binding, or Late Binding
A coding element which involves defining methods in a parent class and overriding them with new implementations in child classes. For example, you could define a method in a parent class and override it in descendant classes as needed. When using an object instantiated from one of these classes, you don't actually need to know which method implimentation is used, you just need to know the name of the method or property to use.
Polymorphism allows the software architect to design a dog.run and a cat.run method and then the programmer can decide at development time whether to instantiate a dog or cat object and either way he knows to call the run method to make the object run. If the designer created a MakeDogRun and a MakeCatRun methods, then the programmer would have a hard time remembering different commands and could not easily substitute one for the other.
Refer to the links below for code examples in various languages.