Given a set of data points $$D \in R^{n+1}$$, assumed to be of the form $$(f(x_1,...,x_n),x_1,...,x_n)$$ we would like to find an appoxiamte function $$f'(x_1,...,x_n)$$ similar to $$f$$. This approximate function $$f'$$ is called the interpolant.
For additional information on interpolation see [http://en.wikipedia.org/wiki/Interpolation interpolation] in wikipedia.