The Linux operating system is a multi-user operating system which allows multiple users to log in and use the computer. To protect the computer (and the privacy of other users), the users' abilities are restricted.
Most users are allowed to run most programs, and to save and edit files stored in their own home folder. Normal users are not normally allowed to edit files in other users' folders or any of the system files. There's a special user in Linux known as the superuser, which is usually given the username root. The superuser has unrestricted access to the computer and can do almost anything.
You won't normally log into the computer as root, but you can use the sudo command to provide access as the superuser. If you log into your Raspberry Pi as the pi user, then you're logging in as a normal user. You can run commands as the root user by using the sudo command before the program you want to run.
For example, if you want to install additional software on Raspbian then you normally use the apt-get tool. To update the list of available software, you need to prefix the apt-get command with sudo:
sudo apt-get update
Find out more about the apt commands.
You can also run a superuser shell by using sudo su. When running commands as a superuser there's nothing to protect against mistakes that could damage the system. It's recommended that you only run commands as the superuser when required, and to exit a superuser shell when it's no longer needed.
It would defeat the point of the security if anyone could just put sudo in front of their commands, so only approved users can use sudo to gain administrator privileges. The pi user is included in the sudoers file of approved users. To allow other users to act as a superuser you can add the user to the sudo group with usermod, edit the /etc/sudoers file, or add them using visudo.