A classic example is water molecules solvating a metal ion. The electronegative oxygen atom contained in the water molecule attracts electrostatically to the positive charge on the metal ion. The result is a 'solvation shell' of water molecules surrounding the ion. This shell can be several molecules thick, dependant on the charge of the ion. With other solvents and solutes, varying steric and kinetic factors can also affect the solvation shell.
Whatever reaction occurs, the solute is said to become solvated by molecules of the solvent, which means that the solvent forms a kind of shell around the solute particles, which is called a solvationshell.
Structures of solvationshells and coordination numbers are both very useful concepts, as they give a direct measure of the solubility of various solutes in water.