Hydrogen Bonding occurs between the charged ions and the polar (having both positive and negative parts) water molecules. Positive ions (cations) will associate with quasi-negatively charged oxygen atom of multiple water molecules and negative (anions) will associate with the quasi-positive charged hydrogens of water molecules. This is what allows things like salt (NaCl) to dissolve in water. The salt disassociates into Na+ and Cl- ions. The Na+ ions attracts a shell of water molecules around due to the attraction between it and the oxygen atoms on the water molecules. Cl- does the same but with the hydrogen atoms. Solid particles already have their + and - parts already neutralized and so don't have any charges to attract the ions.

When you turn the water to steam you are increasing the rate of movement (speed) of the water molecules. They end up moving so fast that they break away from the ions. Imagine tying a magnet to a string, attaching (but not tying) a second magnet to the first and then spinning this over your head. Eventually the second magnet will be flung off the first. Same thing with ion-water bonds. The "flung" ions then begin re-bonding to their original counter ions and these resulting molecules are too big/heavy to evaporate like water does so they are left behind while the water distills away.

-Blast