These coins were minted by the Elven smiths of Eregion and Mirian became the currency of that realm, prized throughout Middle-earth.
As with the Ithildin (Starmoon) with which they marked their doors, Mirian was wrought from Mithril which they traded with the Dwarves for. The currency would commonly be traded between the races at locations such as the market of Khazad-dûm. To honor the Dwarves, Mirian pieces featured Durin's door on one side and its great forge on the other.
In the Second Age, the Dark Lord Sauron relentlessly sought the destruction of Mirian, and now the coins are supremely rare relics of a long-dead Kingdom.