People first mined silver in the Bronze Age, for jewelry. Silver was pretty easy to find all over Europe and West Asia. The big problem was, silver ore (the rocks that had silver in them) generally also had lead in it, so that lead mining and silver mining were the same thing. But lead is very poisonous, so the men who were mining the silver were also being poisoned by the lead. Most lead-and-silver miners died of lead poisoning in two or three years. Because of this, most free men wouldn't work in the mines, and so they forced slaves to work in the mines instead.
Athenian silver coin showing Athena and her owl
One famous silver mine was Laurion, near Athens in Greece. About 500 BC, the Athenians found an enormous silver mine right near Athens, on land that belonged to the government. This mine was what paid to build Athens' first navy, and helped Athens to become a powerful city-state.
Another famous set of mines were in southern Spain. These mines were already being worked in the Bronze Age. After the First Punic War, in the 250s BC, the Carthaginians took over these mines and used the income from them to pay the money the Romans demanded. Then in the Second Punic War the Romans took over these mines and used the money they got from the mines to pay for more conquests.