Alt Gr stands for Alt(ernative) Graphic. It was originally, as you
correctly say, intended for additional keyboard characters, and many
layouts use it for that purpose, with the additional character being
shown to the right of the lower character on the key. The German
keyboard, for example, uses this key for superscript 2 and 3, square
and curly brackets, vertical line (|), backslash, tilde, at symbol
and mu (the Greek letter used for "micro" in units). This means it
can contain all the keys of a standard US/UK keyboard (except for the
pound sterling symbol) plus quite a few others (Umlaute, the "double
s" character, accents, circumflex, section symbol and mu).
It might help you to know that Windows interprets Alt Gr as Alt+Ctrl.
I use this fact in Word to assign additional symbol characters to it.
On your laptop you may be able to reassign some of the Ctrl key
functions to Ctrl+Alt, in effect turning the Alt Gr key into a second
Ctrl key. Some apps, like Word and WordPerfect let you assighn
keyboard shortcuts, or you could get a shareware keyboard mapping
program, which lets you (re)assign keys globally.