1. Introduction to Arduino Core

What is a Core ?

A Core is the software API for a specific group of chips. For example, the Arduino AVR core supports the AVR chips found on most Arduino boards. The SAM3X core supports the Arduino Due, etc. It is the "core" that provides low-level APIs (Application Programmer Interfaces) like analogRead(), digitalWrite(), millis(), etc. which are documented on the Arduino Reference page.

Cores are usually installed as part of a "boards" bundle in the boards manager. This includes definitions for the boards ("variants"), the core and, equally importantly, the compiler and firmware uploading software for the chip on the board. Cores are necessary to make new microcontrollers compatible with your Arduino Software (IDE) and, possibly, the existing sketches and libraries.

In your default IDE installation the Arduino AVR core can be found within the hardware/arduino/avr/cores/arduino folder (Visit the Github Page here ) A screenshot of content inside core/arduino.

Reference : https://www.arduino.cc/en/Guide/Cores

Information

What is the meaning of extension of core: The libraries are used to extend the core. They can be used to provide additional functionalities to the core. Read about Arduino Libraries here.