An overview of radius classes
Radius classes are used when interpolating surfaces. The radius objects define the characteristics of the search radius for calculating the resultant surface.
When predicting a value for a location in an interpolation, a search radius or neighborhood is established because generally as the measured locations get farther from the prediction location they will not be as spatially autocorrelated and will have less influence on the location you are predicting. Thus, you can eliminate those locations that are farther away that have little influence. Not only is there less relationship with locations that are farther away, it is possible that those locations may have a negative influence on the prediction if they are located in an area much different than the prediction location.
The size of the search radius also influences the execution time. The smaller the search radius is, the more quickly the predictions will be made. As a result, it is common practice to limit the number of points that are used when making a prediction through the specifications of the search neighborhood. The identified shape of the neighborhood restricts how far and where to look for the measured values to be used in the prediction. Other neighborhood parameters restrict the point locations that will be used within that shape so, for example, you can define the maximum and minimum number of measured points to use within the neighborhood.
By using the configuration of the valid points within the specified search radius around the prediction location in conjunction with the model fit to the semivariogram, the Kriging tool determines weights for the sample measured locations. From the weights and the values at the sample location, a prediction is made for the unknown value at the prediction location.
ArcGIS Spatial Analyst has two neighborhood types: fixed and variable. A fixed search radius requires a distance and a minimum number of points. The distance dictates the radius of the circle of the neighborhood in map units. The distance of the radius is constant, so, for each interpolated cell, the radius of the circle used to find input points is the same. The minimum number of points indicates the minimum number of measured points to use within the neighborhood. All the measured points that fall within the radius will be used in the calculation of each interpolated cell. When there are fewer measured points in the neighborhood than the specified minimum, the search radius will increase until it can encompass the minimum number of points. The specified fixed search radius will be used for each interpolated cell in the study area. Thus, if your measured points are not spread out equally, there will likely be a different number of measured points used in the different neighborhoods for the various predictions.
With a variable search radius, the number of points used in calculating the value of the interpolated cell is specified. The radius distance varies for each interpolated cell depending on how far it has to search around each interpolated cell to reach the specified number of input points. Some neighborhoods will be small and others will be large depending on the density of the measured points near the interpolated cell. You can specify a maximum distance in map units that the search radius cannot exceed. If the radius for a particular neighborhood reaches the maximum radius before obtaining the specified number of points, the prediction for that location will be performed on the number of measured points within the maximum radius.
Defines a fixed search radius by specifing a distance and a minimum number of points required for analysis. If the required number of points is not found within the specified distance, the search radius will be increased until the specified minimum number of points is found. 

Defines a variable search radius by specifing a maximum distance and the number of points for analysis. If the number of points cannot be satisfied within that maximum distance, a smaller number of points will be used. 
Tools that use radius objects: