The scripting language allows the user to control and influence the behaviour of the game engine. It is in its structure similar to real programming languages. With the large amount of scripting commands you can create dynamic processes happening during a mission. That is, for instance, a camera cutscene or custom interactions between the player and AI units. The scripting engine was designed to be very simple while remaining unlimiting for the scripter.
You don't need any requirements to learn using the scripting language. You should be familiar to mission editing though, as this is the base for any scripting needs.
The first little code in every programming language is usually a small "Hello World" program. It is meant just to display this simple text.
Open up the mission editor, create a custom unit for the player and write the following code into its init line:
hint "Hello World!"
Learning Scripting - A Tutorial
Read the article Introduction to Scripting to get introduced into the scripting language of Armed Assault. You will read, why one needs scripting at all and how the basics work.
Afterwards the article will point you to other articles telling you more about the scripting language.