These curves can be used in a number of ways depending on what your doing, one of the things we commonly do in shaders is use gradients or normalized scalar values (-1 to 1) to control things. These curves give us a way to control the easing on these gradients. For example you could use a simple sine wave to create and ocean wave, you could apply that sine wave gradient to one of these formulas to control the tapering on the waves and influence it’s shape.
You could also use it to control the flow and speed of shader animations. There’s quite a lot of uses depending on what your doing.