An excellent question, one that had me puzzled for a while. Scripts are little programmes that make the game do something. For example, if you wanted a certain jeep to rise 10 feet in the air, bow gracefully and then return to earth, then you could write a script to make it happen. Or if you wanted a Shilka to follow your tank around to give you AA protection. Or if you wanted a good cutscene. Pretty much anything you can think of really.
Read snYpir's excellent Introduction to script snippets in the Ed Depot. For some examples of simple scripts in action download the Tutorial Mission in Tutorials - Getting Started. Also there you will find my Guide to Mission Editing for Beginners, which hopefully you will find helpful.
Scripts are incredibly easy to use, and very easy to create.