Energy is the ability of an object or substance to perform work. In other words, energy is something's ability to create a change in something else.
Mechanical energy can be thought of on a large scale where a change in energy causes some kind of gross movement. For example, if a hockey player takes a slap shot, he or she is transferring the mechanical kinetic energy in the stick to the puck, causing the puck to accelerate.
In the example in the problem, as the water changes phases, it expands and exerts pressure on the vessel. The "gross movement" in this example could be seen in the expansion of the vessel or the turning of a turbine.
Note, in both of these examples, there is no change in the chemical identity of the substances. The puck is still a puck and the water is still water, albeit in a different phase.