Inheritance allows programs developed in an Object Orientated language to reuse code without having it replicated unnecessarily elsewhere within the program.

To achieve this, the programmer has to note generalisations and similarities about various aspects of the program. 

For example, a program could exist to model different forms of transport. At first glance, a car and a train may not have much in common. But abstractly, both will have a speed at which they are travelling, a direction, and a current position.
Methods utilising this data can be specified high up in the inheritance hierarchy, for example in a ‘Transport’ class. For example you could have a method which works out the new position of a train after travelling x minutes in direction y. Likewise, you might want to be able to find out the same information for an object of the type car. 
Inheritance means that if such a method was defined in the superclass of the train and car classes, any car or train object can utilise it. 

The train and car subclasses are said to ‘extend’ the Transport class, as they will have additional characteristics which they don’t share. E.g. passenger capacity would be a class variable of both car and train (but have different values), and a train may have methods along the lines of ‘is toilet engaged’.
If you then wanted to add additional forms of transport, such as an aeroplane, you may wish for that also to have a ‘toilet engaged’ function. Then you could have an extended hierarchy, where a Mass Transport class extends the Transport class. Under which you’d have a train and aeroplane, which would inherit characteristics from both super classes.