Solved What does the ~/. mean?

Files (or directories) beginning with a dot, like .icons are hidden files. Hidden is a bit of a misnomer because they're not really hidden. They just don't show up with a regular ls (they do show with ls -a). The ~ is a shell shorthand for ${HOME} and points to the user's home directory.
The ~ (tilde) is a quick way of specifying your home directory in UNIX.

This means the user you are logged into has a hidden file or folder, specified with (.*) that holds data about icons

Some file system viewers have an option to view these hidden files, such as Nautilus from GNOME

.* files often hold configurations specific to the user, like the registry in Windows, both the window manager and applications can take advantage of this. Applications like eclipse will create a .eclipse in the users home, to give the users settings to the right user. As the desktop manager can use it to store custom configured icons, or the desktop background for the user in some cases.