What does it mean to say that ions are solvated when an ionic substance dissolves in water?

Ions are atoms with defficiency or excess of electrons, i. e. they are particles with charge.

When the ionic compounds are dissolved in water, the ions of the compound separate and each ion is surrounded by molecules of water, that is what it means that the ions are sovated.

This occur because the molecules of water are polar: the oxygen tom in each molecule of water has a partial negative charge and the two hydrogens of water have each a partical positive charge.

So, the negative ions are surrounded by molecules of water whose hydrogen atoms (with partial positive charge) are electrostatically atracted to the negative charge of the ions.

And the positive ions are surrounded by molecules of water whose oxygen atoms (with partial negative charge) are electrostatically attracted to the positive charge of the ions.