Understand administrative privileges
As well as the files that you create, your computer has a number of files which are needed by the system for it to work properly. If these important system files are changed improperly they can cause various things to break, so they are protected from changes by default. Certain applications also modify important parts of the system, and so are also protected.
The way that they are protected is by only allowing users with administrative privileges to change the files or use the applications. In day-to-day use, you won't need to change any system files or use these applications, so by default you do not have administrative privileges.
Sometimes you need to use these applications, so you may be able to temporarily get administrative privileges to allow you to make the changes. If an application needs administrative privileges, it will ask for your password.
Administrative privileges are associated with your user account. Administrator users are allowed to have these privileges while Standard users are not. Without administrative privileges you will not be able to install software. Some user accounts (for example, the "root" account) have permanent administrative privileges. You should not use administrative privileges all of the time, because you might accidentally change something you did not intend to (like delete a needed system file, for example).
In summary, administrative privileges allow you to change important parts of your system when needed, but prevent you from doing it accidentally.
What does "super user" mean?
A user with administrative privileges is sometimes called a super user. This is simply because that user has more privileges than normal users. You might see people discussing things like su and sudo; these are programs for temporarily giving you "super user" (administrative) privileges.
Why are administrative privileges useful?
Requiring users to have administrative privileges before important system changes are made is useful because it helps to prevent your system from being broken, intentionally or unintentionally.
If you had administrative privileges all of the time, you might accidentally change an important file, or run an application which changes something important by mistake. Only getting administrative privileges temporarily, when you need them, reduces the risk of these mistakes happening.
Only certain trusted users should be allowed to have administrative privileges. This prevents other users from messing with the computer and doing things like changing important files. This is useful from a security standpoint.