Melting is the transformation from solid to liquid.
Boiling/evapiration is the transformation from liquid to gas.
If you have some kind of liquid and you heat it up enough it will boil and form bubbles of gas that rise up and escape the bulk liquid.
E.g. watch liquid nitrogen at room temperature. When you heat it from the bottom (or pour it over something at room temperature) it boils just like water.
Bubbles are just pockets of molecules (gas) that have gained enough energy to counteract all the forces inside the liquid (gravity, pressure, electrodynamic, etc) and rise up and escape.
Any liquid at any temperature will,in general, have some molecules that have enough energy to escape. This is just the idea of maxwell-boltzmann distributions. If the liquid is energetic enough then there will be enough highly energetic molecules to form bubbles
So, for example, when you melt ice you get a liquid and that liquid will have molecules of water energetic enough to escape (evaporate)--- though the cooler the liquid the less molecules like this you will have.
Usually water has gasses dissolved in it, like oxygen, nitrogen, etc. These also bubble out (e.g. open a soda and the CO2 bubbles out -though this is a pressure consideration the idea is similar)
Now for a solid like ice you can consider that the colder your sample of ice is the less and less chance you have to find localized areas of melted ice inside the ice cube; and also the lower probability that you will find a gas phase molecule anywhere in your sample.
As the temperature of your sample decreases the probability of finding a molecule in the gas phase approaches zero.
As you increase temperature the probability of finding a gas phase molecules approaches 1 (100%) as the temperature goes to infinity.