Curve functions are used for a variety of purposes in vfx. An example of its use would be an animation curve for the lifespan of a particle; another example would be using a curve to drive a bump map intensity. Listed below is a variety of curves, along with its associated math, that can be used when setting up effects. A mathematical example of a curve function would be
$$ y=1/(1+x^X) $$
A useful website for working with curves is the Math Is Fun Function Grapher.
Easing is the rate of change of a parameter over time. Easing is used to alter the rate of change in a variety of vfx set-ups. Below is a chart of easing functions. Refer to the original website in order to alter some of these and see the code input. Another website, GSGD, demonstrates the programmatic input.
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