Yes, that was simple, wasn't it? The table is at a higher temperature than ice. So, heat flows from the table into the ice.
The animation here shows what happens to the solid particles as you heat ice. The particles begin to vibrate more, and then break away from the solid structure. Then, the molecules are free to move within a fixed volume.

Important: The animation makes it looks like the water molecules are moving inside water (blue background). Remember that the molecules themselves make up water. The blue background is there just to make it easier to see what is going on.