Formula Displacement is the core of the deformer.
It functions in a similar way to the Formula Deformer that comes with Cinema, but with some differences.
The way the deformer works is that, for each point in the spline, a displacement along one or more of the axes is calculated and added to the current spline point coordinate.
An example would be the simplest possible formula, consisting of a single number - '2' - so you would type '2' into the formula fields.
The deformer takes that value and multiplies it by the value in the Amplitude parameter.
If that is the default of 20 units, the result is 2 x 20 = 40.
The value '40' is then added to the point's coordinate value.
If this was added to the Y coordinate, the effect would be to move all the points in the spline along the positive Y axis by 40 units.
With more complex formulas you can do a lot more than that.
The default formula in the deformer is along the Y axis of the point and reads:
A very simple formula, but the effect is to displace the spline along to Y to produce a sine wave.
This image demonstrates the xpTrail generated base spline.