Mobility and flexibility are often used interchangeably, however, they aren't quite the same thing.
Firstly, when we talk about flexibility, it is the length of a muscle and/or how much it can stretch. A typical example of this would be stretching the hamstrings, laying on your back with one leg in the air and holding onto your leg.
Secondly, when talking about mobility, it is generally the range of motion available around a joint. This does include flexibility of muscles and connective-tissue, positioning and strength/stability around the joint to allow for movement. Example of this might be standing up raising one leg in the air… It requires muscles one side of the leg to perform the action, muscles to lengthen on the opposite side and good positioning of the hip and pelvis to allow optimal movement. Hopefully these very brief definitions show that mobility is what we are after for golf and for better movement. Improving mobility can sometimes mean improving flexibility, however, it could be improving joint positioning and strength too. Now, the question is, how do I know what is causing my limited mobility around a joint?! The tricky part can be knowing if it's a flexibility, stability or positioning issue. Firstly, working on all of these could be one place to start (like a shotgun approach). Here are some free videos on YouTube showing plenty of mobility and flexibility exercises to help improve golf. Secondly, you can test… For example, you could perform a shoulder external rotation test in standing and then laying down. Initially, you can look at posture for positioning. If you fail the test both standing and lying down, chances are it's a flexibility issue. However, if you found the test standing but pass laying down it could be a stability issue.
It is pretty obvious that we need some level of Mobility and Flexibility for our golf swing (depending on which style of swing you choose). Turning the hips, trunk and shoulders into the backswing can require more movement than most use in our everyday lives. This can be why many struggle and why it's important to perform exercises habitually to improve these. Check out Golf Fitness On Demand HERE. It includes video workouts/sessions from 5-30 minutes of mobility and flexibility exercises along with strength and power training for golf. And includes videos on how to test mobility and flexibility (like mentioned above).