ListInterpolation[array] constructs an InterpolatingFunction object which represents an approximate function that interpolates the array of values given.
ListInterpolation[array, xmin, xmax, ymin, ymax, ... ] specifies the domain of the grid from which the values in array are assumed to come.
You can replace xmin, xmax etc. by explicit lists of positions for grid lines. The grid lines are otherwise assumed to be equally spaced.
ListInterpolation[array] assumes grid lines at integer positions in each direction.
array can be an array in any number of dimensions, corresponding to a list with any number of levels of nesting.
ListInterpolation[array, domain] generates an InterpolatingFunction object which returns values with the same precision as those in array, domain.
See notes for Interpolation.
See The Mathematica Book: Section 3.8.2.
See also: FunctionInterpolation, ListContourPlot.