Running is the simplest and most effective way to burn up calories. This helps you lose weight (or allows you extra treats)
Regular running reduces your fat percentage and tones your muscle. So you look and feel better.
Your heart gets bigger and more efficient (not to mention more healthy) in response to regular training.
Blood pressure will start to drop within a few weeks of training. That.s healthy!
Your total levels should drop and the ratio of good to bad cholesterol (HDL/LDL) improves with regular training. That is good news!
The impact of running makes your bones more dense (this does not happen in non-weight bearing exercises such as swimming), which becomes more important the older you get. Stronger bones are better.
Regular running has been proven to lower stress levels. Who wants to be stressed?
Regular exercise can improve sleep habits and reduce anxiety. Which is another worry off your mind.
Confidence and self-esteem have been shown to improve in response to regular running, most likely in response to the above health benefits. You can feel better about your raised self-esteem too.
You will improve if you start training, whatever your age. Aside of the health benefits, this gives a great sense of achievement as you improve your ability and fitness. You are still you, just better.