The $\epsilon$-covering number of $B \subseteq \chi$, denoted by $N(\epsilon;B)$, is the size of the smallest set $A \subseteq B$ such that for every $b \in B$ there is an $a \in A$ such that $\rho(a;b) < \epsilon$, where $\rho$ is a Metric on $\chi$.

The $\epsilon$-Packing number gives an upper bound, and the $2\epsilon$-packing number gives a lower bound (this is because removing a point from a $2\epsilon$ packing would result in something that isn't an $\epsilon$ cover, as can be shown using the Triangle inequality)

See here and here

See also UML