Silver in folklore has a lot of different uses. It's the best kind of mirror to use for seeing visions, the best substance to make a bullet to kill a werewolf, even the best kind of stake to use with a vampire in some lore. Why is that though? Well silver was seen to represent purity according to the medieval pseudo science of alchemy. It was often associated with the moon or the sun, and both celestial bodies have significance in rituals for mystical sight according to ancient practices. It's only natural those qualities would stick with the metal throughout its history.
Iron, or cold iron as it's often referred to, has a similar reputation for repelling the supernatural. Often this is interpreted as having a poisonous or dampening effect on the fae and spirits vulnerable to it. Iron horseshoes on doors, iron pokers by cradles, iron knives in doorways were all used to repel evil. Iron fences were put around cemeteries because they were believed to contain restless ghosts inside the holy ground so they could move on. Why it developed these properties in superstitious belief is less clear. Did it represent an earthy groundedness that contrasted with the airy quality of spirits and fae creatures? Was it a consequence of iron becoming more significant in the development of civilization?
Either way, these properties are fun to play with in fantasy. Silver's purity makes it great for channeling magic while iron's repellent qualities can be used as a handy weakness that balances the boundless potential for power that fae creatures have.