How does matter change from solid to liquid?

The addition of heat gives the particles of the solid enough energy to slide past each other.
You can read about the process in
http://socratic.org/questions/how-is-the-melting-point-related-to-the-intermolecular-forces-of-attraction
The particles in a solid are held in position by strong intermolecular forces. The particles can only vibrate back and forth about their equilibrium positions.
When you heat a substance, you add energy to its particles. In the solid, the particles vibrate more violently. The average distance between the particles increases.
Eventually, the particles gain enough energy that they can slide past each other. But they don’t escape from the attractive forces. The solid melts.