Well, to start off, this has nothing to do with domesticating real wild animals. In fact, no animals were (or will be) harmed in any of the actions we do.
The idea of taming chimps comes from a psychological model developed by Professor Steve Peters which places a personified image of a chimp onto the unconscious mind of each person.
All people have their own chimp. Our chimp (or unconscious mind) is responsible for our fight/flight/freeze response. Its primal in nature. It makes the decisions that keep us alive in stressful and dangerous situations. It is incredibly powerful and incredibly fast to respond to situations that we place ourselves in. This is great when we might need to escape from wild animals who's sole intention is to eat us. If we see a bush full of ripe juicy berries as we wander through the forest it will suggest strongly that we stop and eat until there's nothing left as we don't know when our next meal is going to present itself. It is one of the main reasons that humans survived as a species and why we thrive so well in an ever changing world.
In modern living we find ourselves in modern times with very little that actually requires our chimps to step in and take charge. Its unlikely that we'll need to run away from or hide from much to save our lives. The likelihood of having to stand and fight for our lives is very slim. The reality of not knowing when we next may be able to eat has changed.
Our chimps tell us that starting to swim a triathlon with hundreds of other people in the water will result in us being kicked, punched, knocked unconscious, drowned. Our chimps tell us that everyone at the gym is going to be looking at our extra ripples wobbling around as we try to trot on a treadmill or they'll be laughing as we struggle to lift the smallest dumbbell while they easily put the whole bar bending stack over their heads. Our chimps tell us that feeling hungry is the worst possible thing we could feel and to eat all the available sweets just in case a swarm of locusts breaks into the house and gets it all before us.
Our chimps do all these things for various reasons but essentially they don't want us to look bad, feel bad, get hurt, get weak, and a host of other reasons. Our chimps aren't wrong. They aren't being naughty. They aren't being bad. They are simply being chimps and may need some help in understanding why we don't need them to help out and look after us like this all the time. They need working with and teaching to be calm and relaxed in most of these scenarios.
So we need to make some changes. We need to let our inner chimps know that the minor small nut sized stresses of everyday living don't require a sledgehammer response to crack them. The panic feelings that we get that stop us from taking part in an event we've set our minds on or that might keep us from going to the gym or even that might prompt us to eat a whole packet of biscuits in front of the tv are unhelpful and unhealthy for us.
Simply put - We need to tame our chimps.