The whole phrase is indeed the atoms kinetic energy when solids melt to produce liquids.
Structure stiffness and resilience to changes in volume or form define solids. A solid item does not expand like a gas or flow to conform to the geometry of the space it occupies, unlike a liquid, which does both.
Solid matter keeps a constant size and shape, while liquid stuff adapts to the form of its containment while just slightly changing its volume, and gas material expands to take up the intensity and structure of its container.
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