How is computed the train data set score and why? In a lot of machine learning blogs or review, the training dataset accuracy (or other metric) is given alongside the test dataset score. Is this score calculated through the training, or is the training data given at the final model to see if it gives a good score ?

Moreover, what is the point of computing such a score, as the model has been trained with this data ?
Overfitting 

Computing the training score and the test score is usefull to detect overfitting

for exemple here we can see that the training score (in blue) keep improving but at some point the test score (in red) stop improving, that's the sign of overfitting.



But for a final model the training score is not usefull and only the test score should be used.