What is the full form of grub?

Linux

GRand Unified Bootloader

GNU GRUB is a Multiboot boot loader. It was derived from GRUB, the GRand Unified Bootloader, which was originally designed and implemented by Erich Stefan Boleyn.

Briefly, a boot loader is the first software program that runs when a computer starts. It is responsible for loading and transferring control to the operating system kernel software (such as the Hurd or Linux). The kernel, in turn, initializes the rest of the operating system (e.g. GNU).