Your natal chart tells what your aptitudes and stuff as well as the status of what you need to do in life at birth. It will show how you deal with the world and changes, your limitations in life, your areas where you can grow, your ways of thinking aobut the world, your health and energy levels at birth and the tendencies regarding your body, and your creativity and illusions. Many other things can be seen through the lenses of astrology, such as tendencies for insomnia, etc.
Your progressed chart shows how you develop over time as your p=life proceeds. By the time you are thirty years old, most of the goals that were part of your challenges have either been met or not. You progressed chart will show the general challenges that life is offering you, and your ability to deal with these challenges over a period of time of about +/- 4-6 years. It will also show the changes that are wrought in your personality as your Sun and ASC and planets progress into other signs.
For example, I was born with both my sun and ASC in Gemini. When I was around 30, my Sun progressed into Cancer, and the purely intellectual pursuits of my youth translated into the more Cancerian nature of a counseling training into working with children. As I passed 60, my Sun moved out of Cancer and into Leo by progression. I retired from that, and since my sun was no longer in Cancer, I found that after 30 years of counseling children, I had no more interest in doing that.
Dr. Farr notes that progressions are used for prediction, but 2ndary progressions are used also for life development. Solar Arcs, are really called Solar Arc Directions, and they are not really progressions, because all the movements of the planets are based simply on the movement of the Sun. There are also tertiary progressions which can be very useful.
For real predictions, I use Return Charts which and the prediction in the return for the movement of the planet of the return through the chart itself. these are very accurate, and much more precise than progressions since they focus on specific areas of life as represented by the planet in the chart. For the slow outer planets, you can use th 1/12th cycle to great effect.
Hope this helps.