Wat is Gradient boosting, learning rate?

Gradient boosting builds an additive model $F_M(x) = F_0 + \eta\sum_{m=1}^Mh_m(x)$ one tree at a time: tree $h_m$ is fitted to the negative gradient of the loss with respect to the current predictions, $-\partial\ell(y_i, F_{m-1}(x_i))/\partial F$, and added with a factor $\eta\in(0,1]$. The learning rate $\eta$ is the step multiplier of an iterative fit: here the shrinkage of each tree, in gradient descent the size of each step (Book 4, chapter 24). Following the ML convention, $\eta$ denotes it in this book as a local symbol.