The cup that melted the butter the fastest is a good conductor of heat. The cup that melted the butter the slowest is the best insulator (the worst heat conductor).
Substances whose particles have more attraction between them transfer heat slower than substances whose particles move more freely throughout. This is because if particles are moving a greater distance, then they are moving faster, and knocking off of more particles, and also harder therefore giving more of their energy to the other particles. This speeds up the process of conduction.