What is Valence and core electrons?

Example 23.4 (Counting valence electrons)

Oxygen, $1\mathrm{s}^2\,2\mathrm{s}^2\,2\mathrm{p}^4$: outer shell $n = 2$, $2 + 4 = 6$ valence electrons. Sodium, $\ldots 3\mathrm{s}^1$: 1 valence electron. Chlorine, $\ldots 3\mathrm{s}^2\,3\mathrm{p}^5$: 7. Neon, $1\mathrm{s}^2\,2\mathrm{s}^2\,2\mathrm{p}^6$: 8, a full shell.

Example 23.9 (Ions predicted by the rule)

Sodium, $2.8.1$, loses its single valence electron: $\ce{Na+}$, $2.8$, like neon. Magnesium, $2.8.2$, loses two: $\ce{Mg^{2+}}$. Aluminium, $2.8.3$, loses three: $\ce{Al^{3+}}$. Chlorine, $2.8.7$, gains one: $\ce{Cl-}$, $2.8.8$, like argon. Oxygen, $2.6$, gains two: $\ce{O^{2-}}$. Sulfur, $2.8.6$: $\ce{S^{2-}}$. Lithium, $2.1$, loses one and keeps $2$, like helium: $\ce{Li+}$.