There are several ways to approach the topic of premelting, the most figurative way might be thermodynamically. A more detailed or abstract view on what physics is important for premelting is given by the Lifshitz and the Landau theories.
One always starts with looking at a crystalline solid phase (fig. 1: (1) solid) and another phase. This second phase (fig. 1: (2)) can either be vapour, liquid or solid. Further it can consist of the same chemical material or another. In the case of the second phase being a solid of the same chemical material one speaks of grain boundaries. This case is very important when looking at polycrystalline materials.