The Interpolator object is a level object which produces interpolated copies from its sub objects at photorealistic rendering. For example, you can model 1000 sample hairs and render them as 100 000 hairs. 
It is much faster and easier to control the small sample object set as the real amount of hairs. Also, project file size does not grow too much. For many simple geometries, modeling requires much more RAM memory as the rendering. Therefore, the interpolator makes it possible to render much more complex objects.
An interpolation hierarchy example:
interpolalator nurbs curve 1 nurbs curve 2 ...
Interpolation happens between direct sub objects of the interpolator level. Therefore, an interpolator must have at least two sub objects to function. Interpolated sub objects should have identical geometrical structure. In the example above, each nurbs curve must have the same number of points.

The interpolator controls are:
Count  Number of additional render duplicates between each two consecutive sub objects.
Bilinear  Selects bilinear interpolation over consecutive object quadruples. Linear interpolation places duplicates along a straight line between each object pair. Bilinear interpolation places the copies into a rectangular area defined by 4 objects. Therefore, bilinear interpolation method usually fills surfaces better than linear interpolation.
Closed  Selects closed interpolation. Interpolation continues from the last sub object back to the first sub object. The option for is useful for creating circular object groups.
Min and Max Distance  Interpolation happens only when the objects are within the defined range. It does not make sense to interpolate hair between dog's tail and its ear, because the hairs would float in the air.
Random  Additional random variation for interpolated copies. The value defines a maximal random displacement in the current measuring unit. For example, a random value 0.1 displaces points so that each point moves to a random position that is not further than 10 cm away from the original location.