Why do we use extensions while creating the Salesforce Visualforce Page?

A controller extension is an Apex class that extends the functionality of a standard or custom controller. Use controller extensions when:

• You want to leverage the built-in functionality of a standard controller but override one or more actions, such as edit, view, save, or delete.
• You want to add new actions.
• You want to build a Visualforce page that respects user permissions. Although a controller extension class executes in system mode, if a controller extension extends a standard controller, the logic from the standard controller does not execute in system mode. Instead, it executes in user mode, in which permissions, field-level security, and sharing rules of the current user apply.

It is not compulsory to use extension in every vf page.

Hi,

Basically to override the standard functionality or to add some new functionality.

Hope this helps.