Why were coins introduced as money and what were the advantages of this?

It's not only that coins were introduced as money - it's the concept of money, symbolic tokens that somehow carry value.

Coins were chosen for several reasons. First they were usually made of "rare" metals, which meant that they still had a value in themselves (which a bill hasn't), then they were durable, reasonably hard to counterfeit, and within reach of the production technology of the time.

Before the concept of money, trade was through barter, basically trading one kind of merchandise for another. This works fine if you're a fisherman and want to trade a fish for a loaf of bread - but it's not as practical if you want to buy something more substantial. It's also a hassle if the one who've got what you want isn't interested in what you've got - arranging a 3-way barter is much harder. Saving up is also more difficult in a barter culture.

The advantages are mainly as above. Suddenly every one can have something to trade that is of interest to the other - money. The money can be stored to when you need it and it won't spoil.