I learned to meditate about 17 years ago, and nowadays meditate 4 or 5 times a week, as well as going on intensive meditation retreats from time to time. For me, it's an essential part of a busy life - a chance for time to be with myself, to see what's really going on in my body and my mind when all the outside "busyness" stops, and a chance to just be quiet.
How does that relate to healing? Well, you often read that people who meditate have longer attention spans, are better able to deal with stress, and look younger!
I also think that taking that time out to be with yourself is very nurturing in itself - allowing yourself to be sad, angry, happy, joyful, frustrated, or whatever it might be. And just allowing it to be there, without trying to "fix" it. Knowing that we have the capacity to just be with whatever comes up for us is enormously helpful in everyday life.
For meditating on the cushion is like a "practice" for life. If we are able to develop the capacity to stay with what is going on for us in our meditation practice, then we are more likely to be able to do that in our day-to-day life.
From an energetic perspective, staying with our emotions and really feeling them means that we are fully processing whatever happens to us in the present moment. It is when we don't fully feel what is going on for us that we tend to accumulate blockages in our energy field which over time lead to physical illnesses.
It is also the case that in mediation we often feel that a part of our body demands our attention: a pain in our back, or an ache in our head. By gently placing our awareness in this part of the body, and breathing into it, we can gently release any blocked energy there, and the related emotions. This need not be traumatic, and we may not even be aware of what the "story" of the emotions is - and actually we don't need to know in order to release it.
This is the same process as one of the energy healing techniques I have learned. If a client comes to me with a pain in his heart, I can gently place my hand there, and ask him to really feel into the pain. By feeling the pain and the emotions associated with the pain fully, and by accepting them as they are, it is possible to move on. Again, there is no need to know the "story" of the emotional pain: it just is!
Fiona Cutts is an energy healer who specialises in working with clients suffering from ME. You can see more about her work with people struggling with this debilitating condition at http://www.treatmentforme.net/. She has herself recovered from ME using a combination of energy healing, the Emotional Freedom Technique, nutrition, graduated exercise, meditation, chi kung and dance. She is an Integrated Energy Healing, in the tradition of Barbara Brennan, an Advanced Emotional Freedom Technique Practitioner and a reiki practitioner. You can read more about her and the way she works with people suffering from ME at http://www.treatmentforme.net/#/my-story.