FIFA coins are a virtual currency in the FIFA Ultimate Team game mode with which you can buy items, cards and packs for your FUT Club.

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What Are FIFA Coins For?
As a virtual currency, FIFA coins help you to budget your FUT Club for trading and buying items and player/manager cards. With FIFA coins you can buy assets/packs for your club and trade on the Transfer Market.
How to Earn Coins in FIFA 16?
You can make coins in FIFA 16 using the following methods:
Playing FUT Matches
Selling Items on FUT Transfer Market
Selling Items Using Quick Sell Option
Receiving Coins as Gift

Buying and Selling FIFA Coins
Buying and selling FIFA coins are considered against EA Sports Terms of Service, in other words, buying and selling FIFA coins are illegal and by doing this you put your account at risk of getting banned permanently by EA.
Transferring FIFA Coins
Transferring FIFA coins from an account to another is also considered illegal.
FIFA Coins Value and Rate
There is no a fixed value for a FIFA coin in real money. However, if you want to evaluate the effort needed to earn FIFA coins by playing FUT matches, 1 FIFA coin will be estimated at around USD 0.0002. Meaning, $1 is roughly equal to 5,000 FIFA coins. Keep in mind, buying and selling FIFA coins with real money is against EA Sports TOS and it is considered illegal.
FIFA Coins

Where Can I See My FIFA Coins Status?
Your FIFA coins status is visible at the left top of the FIFA 16 Ultimate Team screen where you can see your Club name, number of coins, number of FIFA points and your FUT record