What is meant by 'terminal velocity' for a skydiver, and what forces are acting when a skydiver is falling at terminal velocity?

Upon first exiting the aircraft with the chute closed, gravity is the primary force at work. As the parachutist gains altitude, air resistance also increases until she reaches a point known as "terminal velocity," or roughly 200 km/h, at which point the air resistance force equalizes the gravitational force, causing the parachutist to cease accelerating and descend at a steady speed.

The forces will again balance (when the chute first opens there is a net upward force which slows the downward motion) and the parachutist will fall at the slower velocity. Once the parachute is open, the air resistance is much greater due to the greater surface area, so the new new 'terminal velocity' is much slower, perhaps 20 km/h or so.

The air resistance force is actually very easy to calculate at either of the terminal velocities because it is just the same in an upward direction as the gravitational force in a downward direction; however, during any of the accelerations, it becomes very difficult because it requires fairly sophisticated calculus, knowledge of the shape of what is falling, and a number of other variables.

Terminal velocity for a skydiver is the constant speed reached when the force of gravity pulling the skydiver downward equals the air resistance pushing upward. The forces acting at terminal velocity are gravity pulling downward and air resistance pushing upward.