Legge: You're absolutely right, there is nothing really in the AGS manual. I will be adding a BFAQ entry shortly.
GlobalInts, or Global Integers, are a set of 100 variables that can be accessed anywhere in the game using script. Set a global int with SetGlobalint() and get the value of one with GetGlobalInt().
SetGlobalInt(int variablenumber, int value);
Example: SetGlobalInt(47, 20); will set global int #47 with a value of 20.
Example: GetGlobalInt(47); will return
the value stored in global int #47. Note that this is not a complete command. Treat this like you would a variable; set it to something, or display it somehow. Use it as the object of a command, in other words.
Keep in mind that global ints, like just any other int variable, will only store numbers in the range of -32768 to 32767. There are also GlobalStrings. Look 'em up.