Just as the sigma symbol is used to denote a series: $$\sum_{k=1}^n a_k = a_i + a_2 + a_3 +\cdots+ a_n $$
So too, the big union symbol is used to denote an iteration of disjunctions:
$$\bigcup_{k=1}^n A_k = A_i \cup A_2 \cup A_3 \cup\cdots\cup A_n $$
In this case we interpret the maximum of a disjunction as the maximum term. So: $$\max\Big(\bigcup_{k=1}^n A_k\Big) = \max(A_i , A_2 , A_3 ,\ldots, A_n) $$
Hence:
$$\begin{align} \text{result} & = \max\Big(\bigcup_{A=1}^{L-1}\bigcup_{Z=A}^{L-1}\sum_{i=A}^Z a_i\Big) \\\ & = \max\Big(a_1, (a_1+a_2), \ldots, (a_A+\cdots+a_Z), \ldots, (a_{L-2}+a_{L-1}), a_{L-1}\Big) \end{align}$$