An ionic compound was ions before it ever met the water: a crystal of calcium chloride is a lattice of Ca²⁺ and Cl⁻ held together by attraction. Water pulls the lattice apart and carries the ions off one at a time, and that is dissociation: $\mathrm{CaCl_2(s) \rightarrow Ca^{2+}(aq) + 2\,Cl^-(aq)}$, read aloud: calcium chloride, solid, gives calcium two-plus, aqueous, plus two chloride, aqueous. The (aq) means dissolved in water. Notice what happened to the subscript: the 2 in CaCl₂ counts chloride ions, so it becomes a coefficient, 2Cl⁻, two separate ions. Cl₂⁻ is not a thing.

Three checks make an equation honest. The atoms balance: every atom on the left is on the right. The charges cancel: 2+ against two 1− is zero, because water is neutral and stays that way. And polyatomic ions stay whole: nitrate NO₃⁻, sulfate SO₄²⁻, carbonate CO₃²⁻, phosphate PO₄³⁻, hydroxide OH⁻ and ammonium NH₄⁺ are held together inside by covalent bonds that water does not touch. So $\mathrm{Na_2SO_4 \rightarrow 2\,Na^+ + SO_4^{2-}}$ and $\mathrm{Al_2(SO_4)_3 \rightarrow 2\,Al^{3+} + 3\,SO_4^{2-}}$: the bracket's subscript becomes the sulfate's coefficient, and the sulfate rides through in one piece.