Definition of flexibility to be productive must be restricted to the goal you have.
That statement may seem contradictory. Think about flexibility as a fluid like water. For you to drink the water, or use it for cleaning or irrigation, you must carry it within a container that is usually rigid. Without the rigid container it is difficult to benefit from fluids.
Defining flexibility without a rigid mental structure and a solid goal is not very useful. One definition of flexibility is part of fitness component related to your health. Stretching exercises and joint mobility are part of that structure.
Can you squat down? Bend down and touch your toes? How about reaching behind and touching your shoulder blades? These are all elements of ankle, knee and shoulder flexibility tests. As you test the joints in each area, you would come across overactive and short muscles like calves, hamstring and pecs that take your attention away from the joint and focuses it on the muscle.
When your attention is on the muscle, you may actually damage the joint by moving it out of alignment or overextending it. The beneficial definition of flexibility in physical fitness is built around joint mobility.