Let $\mathscr{G}_{N,M}$ be the family of all graphs with $N$ nodes and $M$ edges. Each $G\in\mathscr{G}_{N,M}$ contains some cliques. Let $c(G)$ be the maximum number of nodes in any clique in $G$. The problem asks you to find
$$\min\\{c(G):G\in\mathscr{G}_{N,M}\\}\;.$$
In words: if a graph has $N$ nodes and $M$ edges, what is the smallest possible size of its largest clique?
A small example may help. Suppose that $N=M=6$. One of the graphs in $\mathscr{G}_{6,6}$ is the graph $G$ consisting of two disjoint triangles; each of those triangles is a clique of size $3$, so $c(G)=3$. But another graph in $\mathscr{G}_{6,6}$ is the circuit $C_6$ of $6$ nodes, like a necklace; its maximal cliques are pairs of adjacent vertices, so $c(C_6)=2$. You can’t have maximal cliques any smaller than that in a graph that has at least one edge, so
$$\min\\{c(G):G\in\mathscr{G}_{6,6}\\}=2\;.$$