I'm currently studying the Global Torelli Theorem for K3 surfaces and I encountered the following section in Huybrechts book.
If $\mathcal{X}\rightarrow S$ is a smooth proper morphism over a connected base $S$ with $X=\mathcal{X}_t$ for some fixed $t \in S$, then the monodromy of this family is the image of the monodromy representation $$\pi_1(S,t) \longrightarrow \operatorname{O}(H^2(X,\mathbb{Z})).$$ By $\operatorname{Mon}(X)$ we denote the subgroup of $\operatorname{O}(H^2(X,\mathbb{Z}))$ generated by the monodromies of all possible families $\mathcal{X}\rightarrow S$ with central fiber $X \simeq \mathcal{X}_t$.
Now, I have never heard of monodromy representation and monodromy before, and I'm struggling looking for a reasonable reference to have the right definition/intuition in the setting I'm in.
First of all, what is the map $\pi_1(S,t) \longrightarrow \operatorname{O}(H^2(X,\mathbb{Z}))$? Is there any good book/article to start with?