What's the function of the Alt Gr key?

IBM named this key "alternate graphic" and it's not a substitute for CTRL + ALT, though CTRL + ALT was implemented as a substitute for ALT GR in Windows. It is a key modifier (like CTRL or SHIFT) that enables a different input than is normally expected of a key.

Depending on your keyboard and location setup, it can be used to produce characters with diacritical marks when used in conjunction with alphabetic keys (most often vowels), and the third symbol that is printed on some keys, for example, € (ALT GR + 4) or ¦ (ALT GR + `) that appear on my UK keyboard. Continental European keyboards generally have many more keys with extra symbols printed on them which correspond letters with the various types of diacritical marks used in those languages.

See AltGr key for more information.

For some keyboards, it allows some alternate combinations. In some keyboards it allows the cent symbol or the euro symbol - Wikipedia has a pretty comprehensive list of combinations using Alt Gr.

However using a US/Windows keymap, it doesn't do anything in most cases.

Also, handy for people with accessibility needs who have to do a Ctrl+alt+del. You try it one-handed.