Passive flexibility refers to the range of motion (ROM) available when an outside force (i.e., gravity, momentum, another body part or another person) is the causative force. Active (dynamic) flexibility is the ROM produced when muscle force (or gravity) creates the movement range. If the muscles are weak, the ROM will be less than it should be. A passive range of motion shows little correlation to an active ROM. Because you exhibit a great ROM in a static position, it does not mean that it relates to what you do when performing actively. The two are not related! If you desire an active range of motion, you must do active stretching. If you desire a static or passive range of motion, then you should do static stretching.
In active stretching, the muscles that are actively involved do so primarily in the eccentric contraction. For example, when you raise your arms overhead as in the lateral arm raise, you are eccentrically stretching the latissimus dorsi and teres major. These muscles undergo an eccentric contraction as you raise the arms to not only control the movement but also to stop the arms from going beyond the capability of the joint.
Another example is to lie on your back and then raise one leg as high as possible. Then lower and raise the other leg and repeat in an alternating manner. Every time you raise the leg, you are using the hip flexor muscles to eccentrically stretch the hamstrings and increase the range of motion in every repetition. You can also use gravity as the force to produce active stretching. For example, if you do a good morning exercise keeping the lower back in its normal slightly arched position as you bend over from the hips, you will elicit an eccentric contraction in the hamstrings. Gravity is responsible for pulling the trunk down and the hamstring muscles need the eccentric contraction to control the down movement.
When you rise up and each time you go down, you should experience a slightly greater ROM. But you do not force an increase in the range of motion. It happens due to the muscle or gravity pulling. Note that these stretches are more natural since they duplicate what occurs in everyday and sports activities.