The label 'y = f(x)' signifies that the vertical axis (y-axis) represents the output values of a function, and the horizontal axis (x-axis) represents the input values. The notation 'f(x)' denotes that the value of 'y' depends on the value of 'x' according to a specific rule or relationship defined by the function 'f'. The curve drawn is the visual representation of all the (x, y) pairs that satisfy this functional relationship.