Flexibility is the ability of muscles (and muscle groups) to lengthen and move a joint through range of motion. Mobility is the ability of a joint to move through range of motion. Movement is a complex marriage of biology: joints, ligaments, tendons, muscles, neurological input and control, pain, medical conditions and medications, and behaviour. So it's important that we are aware of all the different things that can impact movement.
Here's the thing — without flexibility, and strength, bodies are not good at mobility! To move fluidly to the end of a range of motion for a joint the muscle has to comfortably lengthen to it's full extension, and then needs the strength, power, and control to shorten and create flexion.
Flexibility can be a gamechanger for sports dogs, both in the positive aspect and the negative. A dog that vastly lacks flexibility can have a huge impact on being physically able to perform some movements and skills. A dog with too much flexibility can get sore, and easily injured as the joints lack support.
Think about our sports skills. These are complex both in terms of learning and understanding, but also biomechanically what our dogs need to do with their body.