What does "upgrade to 18.04" mean?

What does “dist-upgrade” mean?

It upgrades current OS and installed programs
The process does not affect personal data stored in /home folder
The process will not upgrade the OS version, will not wipe data or settings
It is safe to run it
As you can guess, a backup of personal files is not specially required before an sudo apt dist-upgrade but recommended for general use.

From apt-get manual:

dist-upgrade
   dist-upgrade in addition to performing the function of upgrade,
   also intelligently handles changing dependencies with new versions
   of packages; apt-get has a "smart" conflict resolution system, and
   it will attempt to upgrade the most important packages at the
   expense of less important ones if necessary. So, dist-upgrade
   command may remove some packages. The /etc/apt/sources.list file
   contains a list of locations from which to retrieve desired package
   files. See also apt_preferences(5) for a mechanism for overriding
   the general settings for individual packages.

Backup! Backup! Backup!

Backup your personal data. Bad things can happen any day. And especially on the day you try something on your computer you have never done before.

It will keep your files and applications, and merely upgrade the OS

It will also keep your personal settings and wallpaper. This means if you have been using a different theme, wallpaper etc. to make the desktop your own, the upgrade to a new version of Ubuntu will try to keep as much of those personal modifications as possible. Since upgrade from 16.04 to 18.04 is a move from Unity to Gnome Shell, some personal changes may be incompatible and can't be preserved in the Gnome Shell.

All the applications you installed from the Ubuntu Software application or using the apt command should work. There are a few exceptions such as a software compiled by you, or installed from a PPA may not work until those are updated to work with the new version of the OS.

What is upgraded?

The OS.

All (most) of the default applications that came built into Ubuntu, such as the LibreOffice suite.

There is one "Rule"

Backup your personal data.

How this helps