Eventually, Langlands' ideas crystallized in what is called The Langlands Program and The Langlands Conjectures. Some of its results were crucial to Andrew Wiles' work that led to the proof of Fermat's Last Theorem.
One way of describing the Program is to say that it connects number facts with function facts, much as the factorials are connected to the sine function. (Recall
sin x = x -x^3/3! + x^5/5! -x^7/7!
and n! = n(n-1)(n-2)... 1.) Studying the function's properties will tell you about the number facts, studying the number facts will tell you about the function's behavior.