But I couldn't understand what does $E(n)$ and $E(p)$ mean. I know that it has something to do with sets.
For each state $n \in N$, we maintain a set of states $E(n)$. Eventually, $E(n)$ would contain all states reachable from $n$ via $\epsilon$-transitions.
You can think of $E$ as an array of sets. The notation $E(n)$ just means the value of $E$ at position $n$. So $E(p)$ is just the value of $E$ at position $p$.