Did you ever wonder why sugar dissolves in a cup of coffee? Why not have the sugar just float in the middle of the cup, without dissipating into the coffee?
It's because of the way water molecules interact with molecules in other substances. A water molecule has powerful magnetic properties, because of the two positively charged hydrogen atoms stuck to a negatively charged oxygen atom.
A water molecule can actually break apart the bonds that hold together sugar molecules and insert itself in between them.
This is what's happening on a molecular level when you see the sugar cube getting wet and crumbling apart.
Water molecules are busily inserting themselves between sugar molecules. Eventually they come between all the sugar molecules, dissolving the sugar cube.