Money in World of Warcraft is broken up into three separate types - Gold, Silver and Copper, or a combination of any those types of coins. This medium is used to buy goods and services from players and vendors in the game. Your current total is shown at the bottom right of your open backpack window.
Money is needed to purchase items from vendors, train your character's skills, pay for flight paths, learn how to ride a mount, or acquire a few other generic services like purchasing bank slots. Coins can also be traded to players for goods or services (such as Enchants to weapons or armor), mailed to other characters, used to bid on auctions in the Auction House. or just saved up...perhaps for a specific item, such as a Travelers Mammoth.
Making money, often called farming, can be done several ways, depending on how you like to play the game. It can be looted from defeated mobs, awarded for completing quests, selling items to vendors, or made from other players (either directly or through the Auction House.) Of these, playing the auction house is often considered the most effective. See Auction House for more details.
There are currently three different types of coins used in the game, gold, silver and copper. Copper 1 is the most basic. 100 copper coins equal 1 silver 1. 100 silver is worth 1 gold 1. (So effectively, 1 gold is 10,000 copper.) If you acquire more than 100 copper or silver, it will automatically be converted to the next denomination, rather than forcing you to carry around a ton of small change.
See Currency for more details about coin money and other forms of currency.