An overview of the Interpolation toolset
Surface interpolation tools create a continuous (or prediction) surface from sampled point values.
Visiting every location in a study area to measure the height, concentration, or magnitude of a phenomenon is usually difficult or expensive. Instead, you can measure the phenomenon at strategically dispersed sample locations, and predicted values can be assigned to all other locations. Input points can be either randomly or regularly spaced or based on a sampling scheme.
The continuous surface representation of a raster dataset represents some measure, such as the height, concentration, or magnitude (for example, elevation, acidity, or noise level). Surface interpolation tools make predictions from sample measurements for all locations in an output raster dataset, whether or not a measurement has been taken at the location.
There are a variety of ways to derive a prediction for each location; each method is referred to as a model. With each model, there are different assumptions made of the data, and certain models are more applicable for specific data—for example, one model may account for local variation better than another. Each model produces predictions using different calculations.
The interpolation tools are generally divided into deterministic and geostatistical methods.

The deterministic interpolation methods assign values to locations based on the surrounding measured values and on specified mathematical formulas that determine the smoothness of the resulting surface.
The deterministic methods include IDW (inverse distance weighting), Natural Neighbor, Trend, and Spline.

The geostatistical methods are based on statistical models that include autocorrelation (the statistical relationship among the measured points). Because of this, geostatistical techniques not only have the capability of producing a prediction surface but also provide some measure of the certainty or accuracy of the predictions.
Kriging is a geostatistical method of interpolation.
The remaining interpolation tools, Topo to Raster and Topo to Raster by File, use an interpolation method specifically designed for creating continuous surfaces from contour lines, and the methods also contain properties favorable for creating surfaces for hydrologic analysis.
Explore the following links to learn more about interpolation analysis:
The following table lists the available Interpolation tools and provides a brief description of each.
Tool 
Description 

Interpolates a raster surface from points using an inverse distance weighted (IDW) technique. 

Interpolates a raster surface from points using kriging. 

Interpolates a raster surface from points using a natural neighbor technique. 

Interpolates a raster surface from points using a twodimensional minimum curvature spline technique. The resulting smooth surface passes exactly through the input points. 

Interpolates a raster surface, using barriers, from points using a minimum curvature spline technique. The barriers are entered as either polygon or polyline features. 

Interpolates a hydrologically correct raster surface from point, line, and polygon data. 

Interpolates a hydrologically correct raster surface from point, line, and polygon data using parameters specified in a file. 

Interpolates a raster surface from points using a trend technique. 