Tree decomposition sounds like a dead tree decaying. It is not.
Decomposition tree is the breakdown of a number into multiple parts of that you can understand the number better. My first encounter with Decomposition Tree is in Power BI and I must say that it is really easy to use.
I just delivered a training in Power BI and the participants were glad that they learnt about Decomposition Tree. They prefer it to Pivot Table and told me that they are going to use it.
Decomposition Tree is like presenting the family tree. You will first show the ancestor and then branch out to show the children of the ancestors. And the tree can continue to branch out as you go along. The best way to understand Decomposition Tree is to see the image below.