ponder the diagram above and imagine sliding x to the right at a constant speed. You could even think of x as time; Newton often did. Then the area of the gray region changes continuously as x moves. Because that area depends on x, it should be regarded as a function of x, so we write it as A(x). When we want to stress that this area is a function of x (as opposed to a frozen number), we refer to it as the area accumulation function, or sometimes just the area function.
