Your ability to recognise progress can help support your improvement in any area of development. In most cases a goal for rehab or sports performance may require a big change from where you are to where you want to be. This implies that you will not achieve the change overnight.
In order to progress to your full potential you may have to move through some unpleasant or challenging tasks. Imagine for a moment that you couldn't recognise when you were making progress. Would you be motivated to continue doing those things? You wouldn't think they have been helping because you haven't been able to recognise your progress. I personally would find it almost impossible to continue doing something challenging which I was convinced was not helping at all. On the other hand imagine that you can recognise every little bit of progress you have made no matter how subtle. Then, even while you are a long way from your goal or vision you can still see that you are going in the right direction. This is motivating because you can see that what you are doing is helping you progress. You naturally want to continue with it.
Too often I've seen people improving yet they have not noticed it themselves and their motivation has been suffering or they've given up.
Once you are good at recognising progress and start to focus on this more instead of only on the final outcome, the progress itself can become the source of your motivation more than the final goal. This allows you to continue being motivated long after you have reached your original goal and it also means you might attach less meaning or importance to reaching your goal exactly as you had envisioned it.
In athletic training, fitness and rehab there are many areas in which you can look for progress, and they are often not the main outcome you may be looking for. For example your goal may be to be free of back pain, but first you might recognise progress in your posture, flexibility, strength, movement quality or the ease with which you can do some specific exercises. These can all be stepping stones to your final goal.
A final yet very important note: no single attribute can progress indefinitely. So don't aim for that or expect to see constant progress. This is why it's a great idea to use pre-defined blocks of time (usually measured in weeks or months) to focus on something and then to change to something slightly different for a while. In training this is called periodisation and this is a subject big enough for another article of its own!