An earthen pot contains water inside it. The earthen pot has a number of small pores and holes all around the surface. Water from inside the pot wets the pot, and penetrates through the pores and seeps to the outside surface of the pot.
The water molecules on reaching the outside surface evaporate into the atmospheric air. The difference in pressure between inside the pot and outside the pot makes water molecules come out through the pores.
Water molecules take heat from water inside the pot, from the material of the pot and the atmospheric air. The latent heat of evaporation is thus obtained/absorbed and then water molecules evaporate.
As some heat is absorbed from the pot and water inside, the water inside the pot is much cooler than outside. As the molecules continuously evaporate, the water inside keeps cool even during hot days.