REVISITED: What is an open cover? What exactly is an open cover? Could someone explain it to me like I'm five, and then give a professional answer too?

Here is some literature that may be of interest to any onlooker curious about what an open cover is:

Reference: M.A. Armstrong's Basic Topology
 A: Tommy has a bunch of toys, and Sally has some too, so does Kelly, and Johnny. Now Tommy, Sally, Kelly, and Johnny have their favorite$^1$ toys, you know because some of them they don't like$^2$. If we lay all of everybody's favorite toys on the floor, then we will definitely have all the toys that Joey has$^3$.

$1$: The interior of the set.
$2$: The boundary of the set.
$3$: The set which is covered by the union.

An open cover of a set $E$, in the metric space $\chi$, is a collection of sets $\{G_\alpha\}$ whose union "covers" (contains) $E$, and so, for example if you're given the set $E=\{[1,3]\}$ in the metric space $\chi=(\mathbb{R},d)$, where $d$ is the Euclidean metric, then provided the sets $G_1=\{(0,\frac{3}{2})\}$, $G_2=\{(1,\frac{5}{2})\}$, and $G_3=\{(2,4)\}$ we can say that $\bigcup G_\alpha$ covers $E$.



Above we see that $\{G_\alpha\}$, where $\alpha=1,\dots, 5$, is an open cover of $E$. The green lines denote openness. Note that all sets but $G_5$ are necessary to cover $E$, and as such the union of the sets $G_1, G_2, G_3$, and $G_4$ are a subcover of $\{G_\alpha\}$ as they cover $E$.
A: An open cover of a set $Y$ is a family, (collection), of sets that are open, (a set of open sets), such that $Y$ is a subset of the union of sets in that family. 
Of course when I say "open", I mean that these sets are included in some topology $\mathcal T$ on a space $X$, and $Y \subseteq X$. 
"Union up all the sets in the family", 
"If $Y$ sits inside of that union"
"Then that family is an open cover" 
