On power-on, BIOS starts. BIOS is a piece of code. It is part of motherboard.
BIOS looks for MBR (Master Boot Record) in the boot device. User can customise the location of MBR. For example, you can ask BIOS it to boot from DVD. In this case, MBR present in DVD will be used. MBR is an instruction block which resides at Zeroth address of boot device (DVD in this example). MBR contains the address of GRUB. MBR is a piece of code which instructs BIOS to load GRUB.
MBR loads GRUB. GRUB knows about Linux kernel location. Note that all these info is programmed by Ubuntu Linux team and shipped in bootable Ubuntu ISO.
Since kernel is having control, it performs full load operation of the OS which includes accessing peripheral devices (monitor, USB drive, NIC etc) and OS modules.
After above sequence completion, you are ready to use. Login prompt will appear in general.
This should contain GRUB, linux kernel. Below is an example of /boot content
Grub folder contains GRUB boot loader specific data. vmlinuz-3.19.0-25-generic is the linux kernel.
This will help to detect any problem in the file system.
df command lists disk info.
disk helps to detect any valid partition which might not be showing in df. Below is sample example