A solid is melted and allowed to cool and solidify again. The temperature is measured at equal intervals of time. The graph below shows the change of temperature with time. The part of the curve that is practically horizontal is due to

When a liquid is cooled and reaches its freezing point, the temperature remains constant despite continuous heat loss to the surroundings. This results in a horizontal plateau on the cooling curve [2]. During this phase change from liquid to solid, the substance releases energy known as the latent heat of solidification (or fusion) [1]. This 'hidden' heat is released as intermolecular bonds strengthen, compensating for the heat lost to the environment and preventing a temperature drop until the entire substance has solidified. Once the phase change is complete and all latent heat has been removed, the temperature of the solid begins to decrease again [2]. Specific heat, by contrast, involves temperature changes within a single phase, whereas the horizontal segment specifically represents the transition where latent heat is given away at a constant temperature [2].

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 22: Vertical Distribution of Temperature > Explanation > p. 295
2. [2] https://www.doitpoms.ac.uk/tlplib/phase-diagrams/cooling.php