What does "exaggeration" mean in the context of Boosting?
Not sure, but "exaggeration" could be an other way to talk about "overfitting". 

Boosting are sequential model: each time you build a new tree, it will use the results of the precedent ones, and focus on residuals (where the precedent trees dont perform well). For this, the model exagerate the weights of the precedent mistakes.

If you build too much trees, the last ones will learn on noise, because 
residuals will contains much noise than information. You will have an excellent error rate ("exaggerated error rates") for your train dataset, but if you apply your model on a new dataset, the error will be lower.