Ion
An ion is an atom or group of atoms that has gained or lost electrons and therefore carries a positive or negative electric charge.
Definition
An ion is an atom or group of atoms that carries an electric charge because it has lost or gained electrons; losing electrons makes it positive and gaining them makes it negative. A positive ion is a cation and a negative ion is an anion, and because the imbalance is between protons and electrons, the proton count never changes. Metals tend to form cations and nonmetals tend to form anions, and the opposite charges attract to build ionic compounds. Monatomic ions form when ionization energy or electron affinity favors reaching a noble-gas configuration, while polyatomic ions such as $SO_4^{2-}$, $NO_3^-$, and $NH_4^+$ are covalently bonded groups that carry an overall charge. Ions in solution conduct electricity, and their hydration by polar solvent molecules is what drives dissolution.
Example
A sodium atom gives away one electron and becomes a positive sodium ion, a chlorine atom takes that electron and becomes a negative chloride ion, and together they make salt. Magnesium ($12$ protons) loses $2$ electrons to form $Mg^{2+}$ with $10$ electrons, oxygen ($8$ protons) gains $2$ to form $O^{2-}$ with $10$ electrons, and the two combine as magnesium oxide, $MgO$. Sodium's first ionization energy is $496\text{ kJ/mol}$, but removing a second electron from the $2p$ core costs $4{,}562\text{ kJ/mol}$, which is why sodium forms $Na^+$ and never $Na^{2+}$ in ordinary chemistry; the $Na^+$ ion (radius about $102\text{ pm}$) is far smaller than the neutral atom (about $186\text{ pm}$) because it lost its entire outer shell.
Key Insight
An atom never gains or loses protons to become an ion; only electrons move. The charge on a main-group ion is predictable from its column: group $1$ forms $+1$, group $2$ forms $+2$, group $16$ forms $-2$, and group $17$ forms $-1$, each reaching the nearest full shell. Your nerves fire by moving $Na^+$ and $K^+$ ions across cell membranes and your muscles contract on $Ca^{2+}$ signals, so ion chemistry is the electrical language of living cells, not just the story of salt crystals.