The benefit of Predictive Focus is that it allows a useful estimation of focusing, without the need to autofocus at every field of the scan. This can be a big time saving.
Predictive Focus is a method of interpolating focus positions within a given set of existing focus points. Surveyor contains various algorithms for different mathematical implementations, which is accessed in the Predictive Focus dialog:
Typically the default Multipoint Triangulation is effective for most users and is unlikely to need to be changed.
Each option is given a basic description below, note that the concepts involved are not necessarily easily understood. The term "convex hull" refers to the area between the Predictive Focus points, if they were joined dottodot fashion.

Multipoint Triangulation
This triangulates the points to create a set of planes. If you are outside the convex hull of the points, then it chooses the closest triangle and uses that slope. Outside the hull, the function is discontinuous when it switches triangles, since the triangles will likely be at different slopes and outside the hull they no longer share common sides (in fact they overlap, hence the discontinuity when the closest triangle changes from one to the other).

Triangulation (Extended)
Outside the convex hull, it puts artificial points at each corner of the stage and also at the halfway points along the edge. It then uses the Z of the closest actual PF input point for the Z at each of these points. Then the triangulation is done. This leads to a function that has no discontinuities, but it is essentially flat outside the convex hull and thus you donâ€™t really get any PF adjustments once you are outside the hull.

Triangulation (S/W Only)
This is the same as #1, except that the Oasis DSP is never used.

LeastSquares Plane Fit
This does a least squares fit of the best single plane that fits the input points.

Local Average
This does a local average weighted by the inverse distance of the 3 nearest points.

Interpolate XAxis / YAxis
Straight line interpolation of Z vs. X or Y.

Multipoint + Best from Closest
Same as #1 but outside the convex hull it will: (a) Find the center of gravity of all the points.
 (b) Find the PF input point that is farthest from the COG.
 (c) Find the PF input point that is farthest from the point found in (b).
 (d) Find the PF input point that has the maximum orthogonal distance from the line joining the first two points.

Multipoint + Best from Centroid
Same as #1 but outside the convex hull it will: (a) Find the PF point closes to the current XY position.
 (b) Find the PF input point that is farthest from the point found in (a).
 (c) Find the PF input point that has the maximum orthogonal distance from the line joining the first two points.