What happens when table salt (NaCl) is added to water?

Hydration of the individual ions and formation of discrete aqua complexes, $N {a}^{+} \left(a q\right)$ and $C {l}^{-} \left(a q\right)$.
By most definitions, this is properly considered an example of chemical change, i.e. the formation of new substances, and the making and breaking of strong chemical bonds. We write $N {a}^{+} \left(a q\right)$; in solution we have the hexaqua complexes, ${\left[N a {\left(O {H}_{2}\right)}_{6}\right]}^{+}$ and ${\left[C l {\left({H}_{2} O\right)}_{4 - 6}\right]}^{-}$.