Melting Point
The melting point is the temperature at which a solid changes into a liquid; for a pure substance it is a fixed physical property used for identification.
Definition
The melting point is the exact temperature at which a solid turns into a liquid, and for a pure substance it is the same temperature as the freezing point, the only difference being which direction the change is going; it marks the temperature at which solid and liquid are in equilibrium at a given pressure, so adding heat melts the solid and removing heat freezes the liquid without the temperature itself changing. It is an intensive physical property, independent of sample size, that can identify a pure substance since impurities lower and broaden it, and formally it is the temperature at which solid and liquid have equal Gibbs free energy, $T_m = \Delta H_{fus}/\Delta S_{fus}$, reflecting both the lattice energy overcome on melting and the entropy gained; it shifts with pressure through the Clapeyron equation, $dT/dP = T\Delta V/\Delta H$, rising with pressure for most substances but falling for water, which expands on freezing.
Example
Ice melts at $0^\circ\text{C}$, chocolate melts at about $34^\circ\text{C}$, just below body temperature, which is why it melts in your mouth, and gold melts at $1064^\circ\text{C}$. Sodium chloride melts at $801^\circ\text{C}$ because its ions attract each other strongly, while sucrose melts and decomposes around $186^\circ\text{C}$ and paraffin wax melts near $60^\circ\text{C}$, and across period $3$ of the periodic table melting points rise from sodium ($98^\circ\text{C}$, weak metallic bonding) to silicon ($1414^\circ\text{C}$, network covalent) before falling sharply to phosphorus ($44^\circ\text{C}$), sulfur ($115^\circ\text{C}$), and chlorine ($-102^\circ\text{C}$), all held only by weak dispersion forces.
Key Insight
Tungsten has the highest melting point of any metal, $3422^\circ\text{C}$, which is exactly why it was chosen for light bulb filaments that glow white-hot without melting. Organic chemists relied for a century on a mixed melting point to settle a compound's identity: grinding an unknown with an authentic sample and finding the melting point stays sharp and unchanged proves they are the same substance, while a depressed, broadened range proves they are different, a technique that predates spectroscopy entirely.