If you are wondering what overtraining has to do with stress, then you should understand that training is just another form of stress. Reducing the overall amount of stress in your life can help you train more and recover faster.
To deal with stress effectively you should, of course, know what stress is in the first place. So…
What Is Stress
Stress: a body’s method of reacting to a challenge. 
In this day and age, most people try to avoid stress at all costs, like it’s something bad. But this is not the case. Stress is not only good for you but also necessary for your growth. To understand this concept better, let’s see two more definitions.
Eustress: “good” stress. Stress that has growth potential and can improve your life.
- Working out
- Overcoming challenges
- Learning something new, etc
Distress: the opposite of eustress. It has a negative impact on your health and life.
- Lack of sleep and under-recovery
- Unhealthy diet and lifestyle
- Worrying about the future, etc
Distress can lead to chronic stress, which in effect can lead to disease.
Adaptation is also something crucial in understanding stress. If your body is unable to cope with a stressful situation effectively (and adapt), you move into distress, even if the stimulus is a good one (e.g. over-training).
How Manage Stress Effectively
“People are disturbed not by a thing, but by their perception of a thing” ~ Epictetus 
Some situations are not stressful by themselves, but by how you perceive them. Worrying about the future, for example, will have a stressful effect on you, but that is clearly perceptional. The future is not real, it hasn’t happened. Thinking about past stressful situations is also perceptional and not real. The past doesn’t exist anymore. Worrying about things that out of your control belongs in this category, too. Becoming clear on what the stressor is (real or imaginary) can help you tremendously in managing stress effectively. 
After you have identified the nature of your stress (psychological or physiological), you should start taking action. Removing the physiological stress from your life (e.g. lack of sleep) is not that difficult. You can do this gradually. Start with the biggest stressors and systematically remove them one by one (see exercise below).
Then you can add more of the good stressors, such as training (physical or not). If you are using a good stimulus effectively and thus adapt to it, you are getting more resilient to stress, like in physical training. You are getting stronger each time you train and in a long period of time what used to be a workout becomes a warm up.
Eliminating psychological stress is a bit more tricky than physiological stress, which you can take a direct approach to it. Removing psychological stress is an inside job and requires a different approach. There are different tools and approaches to do this. From my experience, I have found that meditation helps a lot.
Take out a piece of paper (or open a document) and do the following exercise:
- Write down a list of all the stressful activities and situations in your life, both positive and negative.
- In the back page, make a vertical line and put the “good” stressors in the left and the “bad” on the right.
- Go over the “bad” stressor list and order them by putting numbers next to them in terms of importance (effect of stimulus).
- Choose the biggest negative stimulus and make a plan on how to reduce or eliminate it. Remove the stressor gradually over a long period of time, but no longer than it needs to be. For example, if your biggest stressor is the lack of sleep, make a plan on how to take care of it effectively, in the long run. You can start sleeping 15 minutes earlier the first week, then the 30 minutes earlier the 2nd week, etc.. Six months, in my opinion, are more than enough to deal with it effectively (of course this depends on individual factors as well).
As in the example above, it is important to not take this hastily and try to remove everything at once, as this will create a lot of stress and you most likely fail. Furthermore, you should not add any other stressful activities during that period of time. Increasing your physical training, for example, prior to taking care of your sleep completely is not a good idea.
 Wikipedia: Stress (biology)
 The Enchiridion by Epictetus
 Stress and perception (psychological stress) is a very big subject and I can’t cover it whole in a blog post, because of the limited space and expertise. However, I can recommend some resources for those who are interested below.
 “General Adaptation Syndrome And It’s Application In Sport Training” by Natalia Verkhoshansky
 The American Institute of Stress: Daily life stress