What is the transitive and reflective closure of the derivation relationship?
If $R\subseteq A\times A$ is a binary relation, it can be imagined as a directed graph: the elements in $R$ are the edges. The graph however might be infinite. The elements in $R^*$ represent (finite) paths, following zero, one or more of the consecutive edges. Zero edges because of reflexivity, two or more because of transitivity. 

In case of a grammatical derivations the relation $\Rightarrow$ considered is a binary relation in $\Sigma^*\times\Sigma^*$ for some alphabet $\Sigma$, defining a single step as defined by the grammar. Then  $\Rightarrow^*$ consists of all pairs of strings the first one of which can be rewritten into the second, using zero, one or more steps. 

In other words, $x \Rightarrow^* y$ iff there exist steps $x= w_0 \Rightarrow w_1 \Rightarrow \dots \Rightarrow  w_n=y$.
Again, this includes the case of zero steps $x= w_0 = w_n=y$.       

This notation can then be used to define the language of the grammar. Usually [but not always] this looks like $L(G) = \{ x\in\Delta^* \mid S \Rightarrow^* x \}$; the set consisting of all terminal words ($x\in\Delta^*$) that can be derived from the axiom ($S \Rightarrow^* x$).