A parametric curve is a curve that is drawn in "time". In other words, the location (X, Y) (or (X, Y, Z) in 3 space) of a point is based on the "time" at which the curve is being drawn.
The "<<", "Stop", and ">>" buttons cause time to decrement, stop, and increment respectively. This is visuallize in two ways: A black dot moving across the curve itself to portray the position in time of the curve at a given point in time, and a vertical bar which moves across the "B-Spline Basis Functions:" canvas depicting which basis functions are affecting (and to what degree) the curve.
It is perhaps easiest to illustrate the concept of a parametric curve with an example:
Let's create a "straight line". This is actually a curve of order 2.
The linear curve drawn between the two end points of the line can be described by a point, P, which is somewhere between the two lines at any given time (ranging from 0.0 to 1.0). For example, at a time of 0.0, this point P will be at the vertex 0. At time 1.0, point P will be at vertex 1. At time 0.5, P will be halfway between vertex 0 and vertex 1.
To see this on the Curve Educator, do the following. Press the "Clear Curve" button on the "Curve Editor" Panel. On the "B-Spline Basis Functions:" Panel, "Set Order" to 2. Choose "Add Points" on the "Curve Editor" panel, and then create two points using the left mouse button. A straight line should appear between them. Press the ">>" button to see which part of the "curve" is exists at a give time. In the "B-Spline Basis Functions:" panel, you can see how each point affects the curve over time.
At the bottom of the "B-Spline Basis Functions:" canvas, the time at the first knot and the time at the last knot is displayed.