You are right about the energy given off as heat due to the phase change. The material inside in its liquid form is actually what is called a supercooled liquid. That means that at room temperature it would rather be in the solid phase. However, before it can change phases it needs something solid to start growing from. This could be a little piece of dirt or a sharp point on the container that holds the liquid or many other things. This is where the metal disc comes into play. By snapping the disc, the liquid gets the instability it needs and it rapidly changes to a solid, giving off heat.

The material inside most heat pads is called sodium acetate. It is very pure and non-toxic. It is used because it solidifies at 130 Fahrenheit (F) but is also stable enough to stay liquid down to room temperature. This means that when it is a liquid and you snap the disc it will solidify and heat up to 130 F. To return to a liquid requires all the solid to be melted again so you will have to go up above 130 F. Here is a link to a movie that shows the solidification in action:

heat pads in action