standard controller with extension

the below link can provide you the details https://developer.salesforce.com/docs/atlas.en-us.pages.meta/pages/pages_controller_def.htm

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

1. 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.
2. You want to add new actions.
3. 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.

Note:

Although custom controllers and controller extension classes execute in system mode and thereby ignore user permissions and field-level security, you can choose whether they respect a user's organization-wide defaults, role hierarchy, and sharing rules by using the with sharing keywords in the class definition. For information, see “Using the with sharing, without sharing, and inherited sharing Keywords”