How is equation 1 simplified to equation 2 as shown below
I feel like this is basically paraphrasing the explantion in CLRS but maybe it will help.
Let $j$ be the length of the leftmost rod piece in an optimal solution. This piece has a cost of $p_j$ and so it contributes exactly that much to the total revenue. It is easy to see that the remaining part of the rod (of length $n-j$) must be divided up in an optimal manner as well for the whole thing to be optimal
(and thus leads to a revenue of $r_{n-j}$).
Thus, we have $r_n = p_j +r_{n-j} $. Because $r_n$ is the optimal revenue, $r_n \geq \max_{1\leq i \leq n}\{p_i+r_{n-i}\}$. But we also have $r_n = p_j +r_{n-j} \leq \max_{1\leq i\leq n}\{p_i+r_{n-i}\}$.
Putting both ineqalities together gives $r_n = \max_{1\leq i \leq n}\{p_i+r_{n-i}\}$.